Staff Members - Benha University
Absolutely Pure Semimodules
International Journal of Algebra • 2012
Publication Information
Authors
M. Zayed; A. Y. Abdelwanis3
Keywords
absolutely pure semimodule, f-injective semimodule, Field-
house regular semimodule
Journal
International Journal of Algebra
Publisher
Not Available
Volume
6
Issue
Not Available
Pages
Not Available
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
In the present paper, a semimodule M over a semiring R is
called absolutely pure if it is pure in every semimodule containing it as a
subsemimodule. Some well-known properties of absolutely pure modules are
extended to semimodules. We introduce and study two particular subclasses
of absolutely pure semimodules, namely strongly absolutely pure (SAP) and
nitely injective (f -injective) semimodules. When the semiring R is additively
idempotent ,the SAP R
called absolutely pure if it is pure in every semimodule containing it as a
subsemimodule. Some well-known properties of absolutely pure modules are
extended to semimodules. We introduce and study two particular subclasses
of absolutely pure semimodules, namely strongly absolutely pure (SAP) and
nitely injective (f -injective) semimodules. When the semiring R is additively
idempotent ,the SAP R