Publication: On n-1-absorbing prime ideals
Abstract
In this paper, we introduce and study n
-1-absorbing prime ideals of commutative rings. Let R
be a ring and n
a positive integer. A proper ideal I
of R
is said to be an n
-1-absorbing prime ideal if whenever x1x2…xn+1∈I
for some nonunits x1,x2,…,xn+1∈R,
then either x1x2…xn∈I
or xn+1∈I.
It is obvious that 1-1-absorbing (2-1-absorbing) prime ideals are exactly prime (1-absorbing prime) ideals. Various examples and characterizations of n
-1-absorbing prime ideals are given.
Description
Keywords
Matematik, Değişmeli Halkalar ve Cebirler, Temel Bilimler, Mathematics, Commutative Rings and Algebras, Natural Sciences, Temel Bilimler (SCI), Doğa Bilimleri Genel, ÇOK DİSİPLİNLİ BİLİMLER, MATEMATİK, Natural Sciences (SCI), NATURAL SCIENCES, GENERAL, MATHEMATICS, MULTIDISCIPLINARY SCIENCES, Multidisipliner, Ayrık Matematik ve Kombinatorik, Geometri ve Topoloji, Mantık, Fizik Bilimleri, Multidisciplinary, Discrete Mathematics and Combinatorics, Geometry and Topology, Logic, Physical Sciences, Prime ideal1, absorbing prime idealn, 1-absorbing prime ideal
Citation
Ulucak G., Koç S., Tekir Ü., "On n-1-absorbing prime ideals", JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.22, ss.1-11, 2022