|
Modular Pair
In the branch of mathematics called order theory, a modular lattice is a lattice (order), lattice that satisfies the following self-duality (order theory), dual condition, ;Modular law: implies where are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations of the lattice. This phrasing emphasizes an interpretation in terms of projection onto the sublattice , a fact known as the diamond isomorphism theorem. An alternative but equivalent condition stated as an equation (see below) emphasizes that modular lattices form a variety (universal algebra), variety in the sense of universal algebra. Modular lattices arise naturally in algebra and in many other areas of mathematics. In these scenarios, modularity is an abstraction of the Second isomorphism theorem, 2nd Isomorphism Theorem. For example, the subspaces of a vector space (and more generally the submodules of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2d Modular Lattice
D, or d, is the fourth Letter (alphabet), letter of the Latin alphabet, used in the English alphabet, modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is English alphabet#Letter names, ''dee'' (pronounced ), plural ''dees''. History The Semitic languages, Semitic letter Daleth, Dāleth may have developed from the logogram for a fish or a door. There are many different Egyptian hieroglyphs that might have inspired this. In Semitic, Ancient Greek and Latin, the letter represented ; in the Etruscan alphabet the letter was archaic but still retained. The equivalent Greek letter is delta, Delta (letter), Δ. The lower case, minuscule (lower-case) form of 'd' consists of a lower-story left Typeface anatomy#Strokes, bowl and a Typeface anatomy#Strokes, stem ascender. It most likely developed by gradual variations on the upper case, majuscule (capital) form 'D', and is now composed as a stem with a full Typeface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
