A proper prime ideal in the algebra of continuous complex-valued functions on a compact Hausdorff space is dense in a uniquely determined maximal ideal. A quick direct proof of this theorem is obtained using Urysohn's lemma and the Stone-Weierstrass theorem.George...
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 ...
On purely-maximal ideals and semi-Noetherian power series rings Tarizadeh and Aghajani conjectured that each purely-prime ideal is purely-maximal (Tarizadeh and Aghajani in Commun Algebra 49(2):824-835, 2021, Conjecture... N Ouni,A Benhissi - 《Beitrage Zur Algebra Und Geometrie》 被引量:...
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...
Some classes of lattice implication algebras are characterized by their ILI-ideals (respectively prime LI-ideals, maximal LI-ideals). 展开 关键词: Practical, Theoretical or Mathematical/ Boolean algebra multivalued logic/ ILI-ideal maximal LI-ideal lattice implication algebra prime LI-ideal implication...
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....
An ideal I of R is called a d-ideal (f dideal) provided that for each a ∈ I (finite subset F of I) and b ∈ R, Ann(a) Ann(b) (Ann(F) Ann(b)) implies that b ∈ I. It is shown that, the class of z 0 -ideals (hence all sz0 -ideals), maximal ideals in an ...
In Sec. 6 the maximal one-sided and two-sided ideals of π( K) are identified... BS Tam - 《Linear Algebra & Its Applications》 被引量: 30发表: 1981年 On simpleness of semirings and complete semirings one-sided ideal; settling a conjecture and a problem as published by Katsov in 20...
Every nonzero ring contains at least one prime ideal (in fact it contains at least one maximal ideal), which is a direct consequence of Krull's theorem. 每一个非零的交换环都含有至少一个素理想(实际上它含有至少一个极大理想),这是克鲁尔定理的一个直接结果。 WikiMatrix on the terrorist atta...
On the prime, primary and maximal subhypermodules The paper, with the exception of some proofs, is a presentation of results of the authors on the topic of hypermodules in the sense of M. Krasner. The concepts they present are on prime, primary and maximal subhypermodules of a hypermodu...