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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-PWA3-0033-0003

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

On weakly primal ideals (I)

Autorzy Atani, S.  Darani, A. 
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN Let R be a commutative ring with non-zero identity. We say that an element a is an element of R is weakly prime to an ideal I of R if 0 i not equal to ra is an element to I (r is an element to R) implies that r is an element I. If I is a proper ideal of R and w(I) is the set of elements of R that are not weakly prime to I, then we define I to be weakly primal if the set P = w(I) . {0} form an ideal. In this case we also say that I is a P-weakly primal ideal. This paper is devoted to study the weakly primal ideals of a commutative ring. The relationship among the families of weakly prime ideals, primal ideals, and weakly primal ideals of a ring R is considered.
Słowa kluczowe
PL ideały prymalne   pierścienie przemienne   teoria ideałów  
EN primal ideals   commutative ring   ideal theory  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2007
Tom Vol. 40, nr 1
Strony 23--32
Opis fizyczny Bibliogr. 6 poz.
Twórcy
autor Atani, S.
autor Darani, A.
  • Department of Mathematics University of Guilan P.O. Box 1914 Rasht, Iran
Bibliografia
[1] D. D. Anderson, E. Smith, Weakly prime ideals, Houston J. Math. 29 (2003), 831–840.
[2] S. Ebrahimi Atani, F. Farzalipour, On weakly primary ideals, Georgian Math. J. 12 (2005), 423–429.
[3] L. Fuchs, On primal ideals, Proc. Amer. Math. Soc. 1 (1950), 1–6.
[4] L. Fuchs, E. Mosteig, Ideal theory in Prüfer domains, J. Algebra 252 (2002), 411–430.
[5] M. Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1988.
[6] R. Y. Sharp, Steps in Commutative Algebra, London Mathematics Society Student Texts, Cambridge University Press, Cambridge, 1990.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-article-PWA3-0033-0003
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