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A note on the commutativity of rings

100%

Andrzejewski P. , Glanc B.

Demonstratio Mathematica

2006

tom Vol. 39, nr 2

299-303

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].

On weakly primal ideals (I)

86%

Atani S. , Darani A.

Demonstratio Mathematica

2007

tom 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.

Outer Measures on a Commutative Ring Induced by Measures on Its Spectrum

86%

Dudzik D. , Skrzynski M.

Annales Mathematicae Silesianae

2017

tom 31

nr 1

63-70

On a commutative ring R we study outer measures induced by measures on Spec(R). The focus is on examples of such outer measures and on subsets of R that satisfy the Carathéodory condition.