Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

ON WEAKLY PRIMAL IDEALS (I)

ON WEAKLY PRIMAL IDEALS (I) DEMONSTRATIO MATHEMATICAVol. XLNo 12007S. Ebrahimi Atani, A. Yousefian DaraniO N W E A K L Y P R I M A L IDEALS (I)Abstract. Let R be a commutative ring with non-zero identity. We say that anelement a € R is weakly prime to an ideal I of R if 0 ^ ra € I (r £ R) implies that r £ I.If I is a proper ideal of R and w(I) is the set of elements of R that are not weakly primeto / , then we define I to be weakly primal if the set P = w(I) U {0} form an ideal. Inthis case we also say that I is a P-weakly primal ideal. This paper is devoted to studythe weakly primal ideals of a commutative ring. The relationship among the families ofweakly prime ideals, primal ideals, and weakly primal ideals of a ring R is considered.1. IntroductionIn this paper all rings are commutative rings with non-zero identity. Primal ideals in a commutative ring with non-zero identity have been introducedand studied by Ladislas Fuchs in [3] (also see [4]). Weakly prime ideals ina commutative ring have been introduced and studied by D. D. Andersonand E. Smith http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON WEAKLY PRIMAL IDEALS (I)

Download PDF
10 pages

Loading next page...
 
/lp/de-gruyter/on-weakly-primal-ideals-i-0Er7dvmR1G

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© by S. Ebrahimi
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2007-0104
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLNo 12007S. Ebrahimi Atani, A. Yousefian DaraniO N W E A K L Y P R I M A L IDEALS (I)Abstract. Let R be a commutative ring with non-zero identity. We say that anelement a € R is weakly prime to an ideal I of R if 0 ^ ra € I (r £ R) implies that r £ I.If I is a proper ideal of R and w(I) is the set of elements of R that are not weakly primeto / , then we define I to be weakly primal if the set P = w(I) U {0} form an ideal. Inthis case we also say that I is a P-weakly primal ideal. This paper is devoted to studythe weakly primal ideals of a commutative ring. The relationship among the families ofweakly prime ideals, primal ideals, and weakly primal ideals of a ring R is considered.1. IntroductionIn this paper all rings are commutative rings with non-zero identity. Primal ideals in a commutative ring with non-zero identity have been introducedand studied by Ladislas Fuchs in [3] (also see [4]). Weakly prime ideals ina commutative ring have been introduced and studied by D. D. Andersonand E. Smith

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 2007

There are no references for this article.