PlanetMath: graded algebra

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graded algebra

(Definition)

An algebra over a graded ring is graded if it is itself a graded ring and a graded module over such that

$\displaystyle A^p \cdot A^q \subseteq A^{p+q}$

where

, $i \in \mathbb{N}$ , are submodules of

. More generally, one can replace $\mathbb{N}$ by a monoid or semigroup

. In which case,

is called a

-graded algebra. A graded algebra then is the same thing as an $\mathbb{N}$ -graded algebra.

Examples of graded algebras include the polynomial ring being an $\mathbb{N}$ -graded -algebra, and the exterior algebra.

"graded algebra" is owned by mhale. [ full author list (2) | owner history (1) ]

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Cross-references: exterior algebra, polynomial ring, semigroup, monoid, submodules, graded module, graded ring, algebra
There are 9 references to this entry.

This is version 5 of graded algebra, born on 2002-06-07, modified 2007-09-15.
Object id is 3071, canonical name is GradedAlgebra.
Accessed 5621 times total.

Classification:

16W50 (Associative rings and algebras :: Rings and algebras with additional structure :: Graded rings and modules)

Pending Errata and Addenda

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