Prime idealMinimal prime idealMaximal idealTopologyIn this paper, the notion of minimal prime ideal is introduced in residuated lattices and related properties are investigated. Also, new equivalent characterizations and properties for prime and maximal ideals are obtained and the relation between these ...
Locally maximal ideals are prime in a distributive lattice, but not in a general lattice. The aim of this paper is to prove several necessary and sufficient conditions for a locally maximal ideal in a lattice to be prime. Dual of the concept of relative annihilator in a lattice is used to...
Banerjee B., Ghosh S.K., Henriksen M.: Unions of minimal prime ideals of rings of continuous functions on compact spaces. Algebra Universalis 62, 239–246 (2009)MathSciNetCrossRef 9. Blair R.L.: Spaces in which special sets are z-embedded. Canad. J.Math. 28, 673–690 (1984)MathSci...
Some conditions under which prime ideals are maximal are given. 机译:在[Algebra and DiscreteMathematics,2(2003),32–35]中,Kehayopulu N.,Ponizovskii J.和Tsingelis M.表明,在具有身份的交换半群(分别是有序半群)中,每个最大理想都是一个素理想,并且相反,通常情况并非如此。在本文中,我们证明了...
1.This paper generalizes the theories of the minimal prime ideals of a ideal, the maximal 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果。 延伸阅读 极大理想极大理想maximal ...
The ideals in ℤ are principal, so are of the form (n). These ideals are proper if and only if n ≠ 1, and maximal if and only if n > 0 is a prime number. The ideal (0) is prime but is not maximal. By Krull’s theorem (Theorem 2.27), Spec (R) ≠ ∅ if R ≠ {0...
Maximal ideals are zero-dimensional and prime. By convention, prime, primary, and maximal ideals must also be proper, meaning that they are not the entire polynomial ring. The IsProper command can be used to test this condition separately. An optional second argument allows you to override the...
Larson, S.: f -Rings in which every maximal ideal contains finitely many minimal prime ideals. Comm. Algebra 25(12, 3859-3888 (1997)Larson (S.). -- f -Rings in which every maximal ideal contains finitely many minimal prime ideals. Comm. in Algebra, 25 (12), p. 3859-3888 (1997)....
IDEALS (Algebra)ALGEBRAIC fieldsRINGS (Algebra)ZARISKI surfacesSURFACES, AlgebraicR is any ring with identity. Let Specr(R) (resp. Maxr(R), Primr(R)) denote the set of all right prime ideals (resp. all maximal right ideals, all right primitive ideals) of R and let U r(eR)={P∈...
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