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1
Content available remote On weakly primal ideals (I)
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.
2
Content available remote A note on the commutativity of rings
EN
Sufficient conditions for commutativity of rings are proved. They generalize or are related to certain old results due to I. N. Herstein and others, see [1] and [5].
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