Pseudobases in direct powers of an algebra

Author:
Paul Bankston

Journal:
Trans. Amer. Math. Soc. **335** (1993), 79-90

MSC:
Primary 08A35; Secondary 03C05, 12L10

DOI:
https://doi.org/10.1090/S0002-9947-1993-1155348-3

MathSciNet review:
1155348

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Abstract | References | Similar Articles | Additional Information

Abstract: A subset of an abstract algebra is a *pseudobasis* if every function from into extends uniquely to an endomorphism on . is called -*free* has a pseudobasis of cardinality ; is *minimally free* if has a pseudobasis. (The 0-free algebras are "rigid" in the strong sense; the -free groups are always abelian, and are precisely the additive groups of -rings.) Our interest here is in the existence of pseudobases in direct powers of an algebra . On the positive side, if is a rigid division ring, is a cardinal, and there is no measurable cardinal with , then is -free whenever . On the negative side, if is a rigid division ring and there is a measurable cardinal with , then is not minimally free.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1155348-3

Keywords:
Pseudobases,
direct powers,
universal algebra,
minimally free,
fields,
division rings,
measurable cardinals

Article copyright:
© Copyright 1993
American Mathematical Society