Format of Original
American Mathematical Society
Transactions of the American Mathematical Society
Original Item ID
doi: 10.1090/S0002-9947-1993-1155348-3; Shelves: QA1 .A522 Storage S
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 division ring, K is a cardinal, and there is no measurable cardinal u with , then AI is K-free whenever . On the negative side, if A is a rigid division ring and there is a measurable cardinal u with ,then AI is not minimally free.
Bankston, Paul, "Pseudobases in Direct Powers of an Algebra" (1993). Mathematics, Statistics and Computer Science Faculty Research and Publications. 136.
Published version. Transactions of the American Mathematical Society, Vol. 335, No. 1 (January 1993): 79-90. DOI. © 1993 The American Mathematical Society Used with permission.