The notion of a maximal ideal has been introduced and discussed in different studies. We prove several results pertaining to these notions which are versions of their counterparts in classical ring theory. Besides this, we prove that for a commutative ring R, the radical η of an ideal η in...
In this paper, we introduce a special type of prime ideals inMVMV-algebras. We define the concept of aJJ-prime ideal, which is a proper idealIIthat preserves the property of being prime with respect to the idealJJ. IfJJis not a subset ofII, then we call theJJ-prime ideal anNJNJ-prime...
prime ideal is contained in a unique maximal ideal - Sun - 1991 () Citation Context ...ian exchange ring R is a right pm-ring in the sense that every prime ideal of R is contained in a unique maximal right ideal, equivalently, every prime ideal is contained in a uniquemaximal ideal....
We also show that it is possible for commutative semiprime f-rings with identity element to have the property that every maximal -ideal has finite rank while the f-ring does not have finite rank. Rings of continuous functions of finite rank are studied. Some sufficient conditions are given ...
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It is far from true that decomposition into prime factors is unique in all rings. Thus the result of Problem 1 shows that among orders in algebraic number fields, unique factorization can occur only for maximal orders. Unique factorization for the ring Z of rational integers follows from the ...
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showed that in commutative semigroups (resp. ordered semigroups) with identity, every maximal ideal is a prime ideal and the converse is not true in general. In this note we prove that for an ordered semigroup S satisfying S = (S~2] all maximal ideals are weakly prime ideals. This ...
Attention is paid, inparticular, to invertible maximal ideals and to invertible minimal (non-zero) prime ideals.It is with respect to an invertible maximal and minimal prime ideal that a local decompo-sition into a partial fraction, the "principal part", and a "regul r part" is obtained ...
1) maximal prime ideal 极大素理想 1. This paper generalizes the theories of the minimal prime ideals of a ideal, themaximal prime ideals of a ideal in the commutative rings to DQC rings. 将交换环中关于一个理想的极小素理想和极大素理想的两种理论推广到DQC一环中,得到了与交换环中相近的重要结...