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Ideals
Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considered in abstract algebra * Ideal, special subsets of a semigroup * Ideal (order theory), special kind of lower sets of an order * Ideal (set theory), a collection of sets regarded as "small" or "negligible" * Ideal (Lie algebra), a particular subset in a Lie algebra * Ideal point, a boundary point in hyperbolic geometry * Ideal triangle, a triangle in hyperbolic geometry whose vertices are ideal points Science * Ideal chain, in science, the simplest model describing a polymer * Ideal gas law, in physics, governing the pressure of an ideal gas * Ideal transformer, an electrical transformer having zero resistance and perfect magnetic threading * Ideal final result, in TRIZ methodology, the best possible solution * Thought experiment, sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ring Theory)
In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group. Among the integers, the ideals correspond one-for-one with the non-negative integers: in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. However, in other rings, the ideals may not correspond directly to the ring elements, and certain properties of integers, when generalized to rings, attach more naturally to the ideals than to the elements of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (order Theory)
In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion. Ideals are of great importance for many constructions in order and lattice theory. Basic definitions A subset of a partially ordered set (P, \leq) is an ideal, if the following conditions hold: # is non-empty, # for every ''x'' in and ''y'' in ''P'', implies that ''y'' is in ( is a lower set), # for every ''x'', ''y'' in , there is some element ''z'' in , such that and ( is a directed set). While this is the most general way to define an ideal for arbitrary posets, it was originally defined for lattices only. In this case, the following equivalent definition can be given: a subset of a lattice (P, \leq) is an ideal if and only if it is a lower set that is closed under finite joins ( suprema); that is, it is non ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (set Theory)
In the mathematical field of set theory, an ideal is a partially ordered collection of sets that are considered to be "small" or "negligible". Every subset of an element of the ideal must also be in the ideal (this codifies the idea that an ideal is a notion of smallness), and the union of any two elements of the ideal must also be in the ideal. More formally, given a set X, an ideal I on X is a nonempty subset of the powerset of X, such that: # \varnothing \in I, # if A \in I and B \subseteq A, then B \in I, and # if A, B \in I then A \cup B \in I. Some authors add a fourth condition that X itself is not in I; ideals with this extra property are called . Ideals in the set-theoretic sense are exactly ideals in the order-theoretic sense, where the relevant order is set inclusion. Also, they are exactly ideals in the ring-theoretic sense on the Boolean ring formed by the powerset of the underlying set. The dual notion of an ideal is a filter. Terminology An element of an ide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (Lie Algebra)
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity. The Lie bracket of two vectors x and y is denoted ,y/math>. The vector space \mathfrak g together with this operation is a non-associative algebra, meaning that the Lie bracket is not necessarily associative. Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: any Lie group gives rise to a Lie algebra, which is its tangent space at the identity. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to finite coverings ( Lie's third theorem). This correspondence allows one to study the structure and classification of Lie groups in terms of Lie algebras. In physics, Lie groups appear as symmetry groups of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal (ethics)
An ideal is a principle or value that one actively pursues as a goal, usually in the context of ethics, and one's prioritization of ideals can serve to indicate the extent of one's dedication to each. The belief in ideals is called ethical idealism. In some theories of applied ethics, such as that of Rushworth Kidder, there is importance given to such orders as a way to resolve disputes. In law, for instance, a judge is sometimes called on to resolve the balance between the ideal of truth, which would advise hearing out all evidence, and the ideal of fairness. Given the complexity of putting ideals into practice, and resolving conflicts between them, it is not uncommon to see them reduced to dogma. One way to avoid this, according to Bernard Crick, is to have ideals that themselves are descriptive of a process, rather than an outcome. His political virtues try to raise the practical habits useful in resolving disputes into ideals of their own. A virtue, in general, is an ideal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Type
Ideal type (german: Idealtypus), also known as pure type, is a typological term most closely associated with sociologist Max Weber (1864–1920). For Weber, the conduct of social science depends upon the construction of abstract, hypothetical concepts. The "ideal type" is therefore a subjective element in social theory and research, and one of the subjective elements distinguishing sociology from natural science. Meaning An ideal type is formed from characteristics and elements of the given phenomena, but it is not meant to correspond to all of the characteristics of any one particular case. It is not meant to refer to perfect things, moral ideals nor to statistical averages but rather to stress certain elements common to most cases of the given phenomenon. It is also important to pay attention that in using the word "ideal" Max Weber refers to the world of ideas (german: Gedankenbilder, "mental images") and not to perfection; these "ideal types" are idea-constructs that hel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Chain
Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considered in abstract algebra * Ideal, special subsets of a semigroup * Ideal (order theory), special kind of lower sets of an order * Ideal (set theory), a collection of sets regarded as "small" or "negligible" * Ideal (Lie algebra), a particular subset in a Lie algebra * Ideal point, a boundary point in hyperbolic geometry * Ideal triangle, a triangle in hyperbolic geometry whose vertices are ideal points Science * Ideal chain, in science, the simplest model describing a polymer * Ideal gas law, in physics, governing the pressure of an ideal gas * Ideal transformer, an electrical transformer having zero resistance and perfect magnetic threading * Ideal final result, in TRIZ methodology, the best possible solution * Thought experiment, sometimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', denotes the result of applying the semigroup operation to the ordered pair . Associativity is formally expressed as that for all ''x'', ''y'' and ''z'' in the semigroup. Semigroups may be considered a special case of magmas, where the operation is associative, or as a generalization of groups, without requiring the existence of an identity element or inverses. The closure axiom is implied by the definition of a binary operation on a set. Some authors thus omit it and specify three axioms for a group and only one axiom (associativity) for a semigroup. As in the case of groups or magmas, the semigroup operation need not be commutative, so ''x''·''y'' is not necessarily equal to ''y''·''x''; a well-known example of an operation that is as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
An Ideal
''An Ideal'' () is the third studio album by Chinese singer-songwriter Ronghao Li, released on January 22, 2016, by Warner Music Taiwan Warner Music Group's labels include the following. Flagship labels *Atlantic Records *Elektra Records *Parlophone Records *Warner Records Atlantic Records Group * 1st & 15th Entertainment * All Money In * Artist Partners Group * Asylum Re .... The album contains 11 songs, with the album's total length being 53:04 minutes. Information The following is the official comment on An Ideal's release: "Staying ordinary in an extraordinary world, with his (Ronghao Li) music, slowly disintegrating the veil of lies we've been wearing. They call it an ideal, something extraordinary, but at the same time ordinary. Even though stumbled over rocks and lost our ways in the mist, it doesn't mean it's over. Living in the day, living in the night, venturing through this metropolis, we all see things with our own way. But why not observe our world with R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Changhe Ideal
The Changhe Ideal is a city car produced by Jiangxi Changhe Suzuki Automobile Company, in a joint-venture between Chinese and Japanese automakers Changhe and Suzuki, since 2003. The model is known in Brazil as the Effa M100, in Uruguay as the Effa Ideal and in Italy as Martin Motors Ideal 1000. Overview The Ideal was designed by Bertone, available initially with a 1.1-litre gasoline engine and safety items such as anti-lock braking system and airbags. It was facelifted in 2006, when it received new lights, a new grille and an updated interior. The Ideal was sold in Colombia as taxi mainly in 2009 and 2010, but due to the lack of quality most vehicles are out of service today. NICE Ze-O NICE Car Company presented an electric version of the Ideal called the NICE Ze-O at the 2008 British International Motor Show, but a production version was not forthcoming. NICE shortly after went into administration and was acquired by Aixam-Mega. Gallery File:Changhe Ideal.jpg, Changhe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Mini School
Ideal Mini School is a public secondary mini school in Vancouver, British Columbia. It is a complete grade 8–12 high school program. It is generally accepted as the "steward school" of Sir Winston Churchill Secondary, although it was run independently under the leadership of head teacher Jim King, who was replaced by Ernie Pao in September 2014. The current head teacher is Sandra Hatzisavva. Entrance An English and cognitive skills test is taken by prospective students as part of the application process. Community service, grades, and extra-curricular activities are also considered. Interviews with candidates are conducted to further narrow the pool of applicants. Program Other than in its small size, Ideal differs from Churchill Secondary in its enriched approach to learning. It offers an intimate and creative environment, and utilizes an informal teaching style where teachers are addressed by their first names and student-teacher trust is held in high esteem. Integration a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal, South Dakota
Ideal is an unincorporated community in northern Tripp County, South Dakota, United States. It lies north of the city of Winner, the county seat.Rand McNally. ''The Road Atlas '05.'' Chicago: Rand McNally Rand McNally is an American technology and publishing company that provides mapping, software and hardware for consumer electronics, commercial transportation and education markets. The company is headquartered in Chicago, with a distribution ..., 2005, p. 93. Its elevation is 1,886 feet (575 m). The population of the CDP was 86 at the 2020 census. Ideal's town site was considered to be "ideal" for farming, hence the name. Demographics References Unincorporated communities in Tripp County, South Dakota Unincorporated communities in South Dakota {{SouthDakota-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
