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] |
| Βάση Δεδομένων: |
Academic Search Index |