The second main result of this paper is a proof that the assignment to each ring of the maximal ideal space is functorial on the category of weakly symmetric rings satisfying (1) and ring homomorphisms.Shu-HaoSunSDOSJournal of Pure & Applied Algebra...
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prime idealordered semigroupIn [Algebra and Discrete Mathematics, 2 (2003), 32–35], Kehayopulu N., Ponizovskii J. and Tsingelis M. showed that in commutative semigroups (resp. ordered semigroups) with identity, every maximal ideal is a prime ideal and the converse is not true in ...
S. Larson, f-rings in which every maximal ideal contains finitely many minimal prime ideals, Comm. Algebra, 25(12) (1997) 3859-3888.S. Larson, f -Rings in which every maximal ideal contains finitely many minimal prime ideals, Comm. Algebra 25(12) (1997), 3859-3888....
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 ...
2. 质理想 ...),因此我们亦可以定义相关的「理想」概念,包括「质理想」(Prime Ideal)、「极大理想」(Maximal Ideal)等。 chowkafat.net|基于2个网页 3. 理想集合 一个理想集合 I 叫 质理想集合(prime ideal),如果 I 满足 episte.math.ntu.edu.tw|基于 1 个网页...
The module in which, weakly prime submodules and the prime submodules coincide, are studied, and it is shown that multiplicative modules have this property called compatibility property. It is also shown that each R-module is compatible if and only if each prime ideal is maximal or if and ...
then we call theJJ-prime ideal anNJNJ-prime ideal. We investigate the relationships between these ideals and their connections to minimal prime ideals and maximal ideals. Additionally, we explore various properties such as extension, transitivity, meet, join, and annihilator. Finally, we study prime...
Joe L. Mott and Kermit Rose, Prime-producing cubic polynomials, Ideal theoretic methods in commutative algebra (Columbia MO 1999) 281–317, Lecture Notes in Pure and Appl. Math., 220 Dekker, New York, 2001; MR 2002c: 11140. Google Scholar Gerry Myerson, Problems 96:16 and 96:17, Wes...
In every Euclidean ring, factorization into primes is unique. Consider as an example the maximal order D of the quadratic field R(√−1). We shall show that D has the division with remainder property with ||α|| = N(α). Let α and β≠ 0 be arbitrary numbers of D. Then αβ...