Algebra theory MOC

Graded algebra

Let be a monoid. An algebra over is said to be -graded iff it is an -graded vector space such that #m/def/ralg

for any . If is a -monoid, this definition is equivalent to that of a graded ring, and hence .

Category of graded algebras

Many of our typical algebra constructions carry over. These motivate .

• Graded algebra homomorphism
• Graded subalgebra, Quotient graded algebra

Properties

• If , the degree operator on is a derivation.
• If is commutative, then must be abelian/

Examples

• Tensor algebra

See also

• Graded structure

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