APS of algebras

From Apstheory

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Current revision as of 03:03, 30 December 2006

[edit] Definition

[edit] Symbol-free definition

An APS of algebras over a base ring is an APS of rings, each of which is an algebra over the base ring, such that the block concatenation maps are algebra homomorphisms.

[edit] Definition with symbols

An APS Failed to parse (Can't write to or create math temp directory): (G,\\Phi)

of algebras over a base ring Failed to parse (Can't write to or create math temp directory): R
is an APS of rings where each member Failed to parse (Can't write to or create math temp directory): G_n
is a Failed to parse (Can't write to or create math temp directory): R

-algebra and the block concatenation map Failed to parse (Can't write to or create math temp directory): G_m

× Failed to parse (Can't write to or create math temp directory): G_n
→ Failed to parse (Can't write to or create math temp directory): G_{m+n}
is a Failed to parse (Can't write to or create math temp directory): R

-algebra homomorphism.

Further information: APS of rings