On weakly primal ideals (I)

• Autorzy: Atani S. , Darani A.
• 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

EN

primal ideals; commutative ring; ideal theory

PL

ideały prymalne; pierścienie przemienne; teoria ideałów

• 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.