PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE MODULES

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NIKSERESHT ASGHAR

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Seminar Paper

Paper Information

Seminar: IRANIAN ALGEBRA SEMINAR
Year:2009 | Issue:20

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Information Seminar Paper

Title

PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE MODULES

Author(s)

NIKSERESHT ASGHAR

Keywords

PRESIMPLIFIABLE MODULES

WEAKLY PRESIMPLIFIABLE MODULES

ASSOCIATES

ZERO DIVISORS

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.

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Cite

APA: Copy

NIKSERESHT, ASGHAR. (2009). PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE MODULES. IRANIAN ALGEBRA SEMINAR. SID. https://sid.ir/paper/904450/en

Vancouver: Copy

NIKSERESHT ASGHAR. PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE MODULES. 2009. Available from: https://sid.ir/paper/904450/en

IEEE: Copy

ASGHAR NIKSERESHT, “PRESIMPLIFIABLE AND WEAKLY PRESIMPLIFIABLE MODULES,” presented at the IRANIAN ALGEBRA SEMINAR. 2009, [Online]. Available: https://sid.ir/paper/904450/en

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