Even subalgebra

Even subalgebra

Let ${\displaystyle A}$ be a superalgebra over a commutative ring ${\displaystyle K}$. The submodule${\displaystyle A_{0}}$, consisting of all even elements, is closed under multiplication and contains the identity of ${\displaystyle A}$ and therefore forms a subalgebra of ${\displaystyle A}$, naturally called the even subalgebra. It forms an ordinary algebra over ${\displaystyle K}$.