Paper Information

Title:  PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE MODULES
Type: PAPER
Author(s): NIKSERESHT ASGHAR*
 
 *DEPARTMENT OF MATHEMATICS, SHIRAZ UNIVERSITY SHIRAZ 71454, IRAN
 
Name of Seminar: SEMINAR ON ALGEBRA (SALG20)
Type of Seminar:  CONFERENCE
Sponsor:  TARBIAT MOALLEM UNIVERSITY, FACULTY OF MATHEMATICAL SCIENCES AND COMPUTER
Date:  2009Volume 20
 
 
Abstract: 

In [2] it was noted that in commutative rings with zero divisors the equivalent definitions of associates in integral domains are not equivalent anymore and thus lead to different types of irreducible elements. There it was proved that in such rings these different types of associates are equivalent if and only if the ring, R, is presimplifiable, that is for every r, aÎR, ra=a implies a = 0 or rÎU(R). In [3] they extended the basic definitions of the theory of factorization to modules; including presimplifiablity. Here we define the weakly presimplifiable condition for modules. This notion enables us to reduce checking presimplifiablity and several other factorization properties in general modules to checking them just in faithful modules. Also we study how these properties behave under several module constructions.

 
Keyword(s): PRESIMPLIFIABLE MODULES, WEAKLY PRESIMPLIFIABLE MODULES, ASSOCIATES, ZERO DIVISORS
 
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