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On weakly primal ideals (I)

Atani S., Darani A.

Demonstratio Mathematica

2007

Vol. 40, nr 1

23-32

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.