Pseudobases in Direct Powers of an Algebra

Authors

Paul Bankston, Marquette UniversityFollow

Document Type

Article

Language

eng

Publication Date

1-1993

Publisher

American Mathematical Society

Source Publication

Transactions of the American Mathematical Society

Source ISSN

0002-9947

Original Item ID

DOI: 10.1090/S0002-9947-1993-1155348-3

Abstract

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 A^I 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 A^I is K-free whenever . On the negative side, if A is a rigid division ring and there is a measurable cardinal u with ,then A^I is not minimally free.

Comments

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.

Recommended Citation

Bankston, Paul, "Pseudobases in Direct Powers of an Algebra" (1993). Mathematics, Statistics and Computer Science Faculty Research and Publications. 136.
https://epublications.marquette.edu/mscs_fac/136