✦ LIBER ✦

Generalized Pure Modules

✍ Scribed by John Dauns

Book ID: 102572997
Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 169 KB
Volume: 242
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8793

No coin nor oath required. For personal study only.

✦ Synopsis

For right modules M < N over a ring R, consider any system of equations in M of the form

The usual definition of M as pure in N is that for any such a finite system, if the system is solvable in the bigger module N, then it is already solvable in M. Here the above ordinary concept of purity will be generalized by allowing I and J to be of possibly infinite cardinalities I < µ and J < ℵ for fixed cardinals µ and ℵ. In this way, generalized µ < ℵ < -pure and absolutely pure concepts are defined in terms of µ and ℵ and studied. Here the number ℵ of relations of a module is simultaneously studied with the more familiar number µ of generators.

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