Nil-prime ideals of a commutative ring.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	Nil-prime ideals of a commutative ring.
Συγγραφείς:	Farshadifar, Faranak¹ (AUTHOR) f.farshadifar@cfu.ac.ir
Πηγή:	Communications in Algebra. Aug2026, p1-7. 7p.
Θεματικοί όροι:	Prime ideals, Ideals (Algebra), Commutative rings, Algebra, *Ring theory
Περίληψη:	AbstractLet R be a commutative ring with identity and Nil(R) be the set of all nilpotent elements of R. The aim of this paper is to introduce and study the notion of nil-prime ideals as a generalization of prime ideals. We say that a proper ideal P of R is a nil-prime ideal if there exists x∈Nil(R) such that whenever ab∈P, then a∈P or b∈P or a+x∈P or b+x∈P for each a,b∈R. Also, we introduce nil versions of some algebraic concepts in ring theory such as nil-maximal ideal, nil-minimal ideal, nil-principal ideal and investigate some nil-version of a well-known results about them. [ABSTRACT FROM AUTHOR]
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