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...
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 ...
Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules Classifications of prime, primitive, completely prime, and maximal ideals are given for the algebra U .doi:10.1063/1.4973378V. V. Bavula... VV Bavula,T Lu - 《Journal of Mathemat...
Prime ideals are maximal if allrrsatisfyrnr=rrnr=rfor somenr>1nr>1 Ask Question Asked12 years, 1 month ago Modified2 months ago Viewed5k times 18 LetRbe a commutative ring with an identity such that for allr∈r∈R, there exists somen>1n>1such thatrn=rrn=r. Show that any...
6) 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...
A maximal ideal (x,y) is a type of primary ideal, as it is a prime ideal that is not contained in any other ideal. Additionally, primary ideals can be decomposed into a product of maximal ideals, which is known as the primary decomposition theorem. How are maximal ideals and primary id...
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...
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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...