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Pseudobases In Direct Powers Of An Algebra, Paul Bankston
Pseudobases In Direct Powers Of An Algebra, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
A subset P of an abstract algebra A is a pseudobasis if every function from P into A extends uniquely to an endomorphism on A. A is called K-free has a pseudobasis of cardinality K; A is minimally free if A has a pseudobasis. (The 0-free algebras are "rigid" in the strong sense; the 1-free groups are always abelian, and are precisely the additive groups of E-rings.) Our interest here is in the existence of pseudobases in direct powers AI of an algebra A. On the positive side, if A is a rigid …