Results 1 to 10 of about 58,134 (302)

Maximal Ideal and Prime Ideal in an L-lattice [PDF]

Fuzzy Information and Engineering
In this paper, the notions of an L-sublattice, L-ideal, and L-dual ideal of an L-lattice are introduced. The concepts of an L-maximal ideal and an L-prime ideal in an L-lattice are also defined. The present paper also gives the precise structures of an L-
Aparna Jain, Iffat Jahan
doaj   +3 more sources

A Prime Ideal Principle for Two-Sided Ideals [PDF]

Communications in Algebra, 2016
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a “Prime Ideal Principle” that gives a uniform method of proving such facts, generalizing the Prime Ideal ...
Manuel L Reyes
exaly   +7 more sources

Associated Prime Ideal and Minimal Prime Ideal of an Ideal of an L-Subring

Fuzzy Information and Engineering, 2023
In this paper, a systematic theory for the ideals of an L-ring L(μ,R) has been developed. Earlier the authors have introduced the concepts of prime ideals, semiprime ideals, primary ideals, and radical of an ideal in an L-ring.
Anand Swaroop Prajapati, Naseem Ajmal, Iffat Jahan   +2 more
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On Neutrosophic Soft Prime Ideal [PDF]

Neutrosophic Sets and Systems, 2018
The motivation of the present paper is to extend the concept of neutrosophic soft prime ideal over a ring. In this paper the concept of neutrosophic soft completely prime ideals, neutrosophic soft completely semi-prime ideals and neutrosophic soft prime ...
Tuhin Bera, Nirmal Kumar Mahapatra
doaj   +2 more sources

Prime ideal on the end_Z (Z^n ) Ring

Al-Jabar, 2022
The set of all endomorphisms over -module  is a non-empty set denoted by . From  we can construct the ring of  over addition and composition function. The prime ideal is an ideal which satisfies the properties like the prime numbers.
Zakaria Bani Ikhtiyar, Nikken Prima Puspita, Titi Udjiani   +2 more
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Prime ideal graphs of commutative rings

Indonesian Journal of Combinatorics, 2022
Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP.
Haval Mohammed Salih, Asaad A. Jund
doaj   +3 more sources

Fuzzy Prime Ideal Theorem in Residuated Lattices

International Journal of Mathematics and Mathematical Sciences, 2021
This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization.
Pierre Carole Kengne, Blaise Blériot Koguep, Celestin Lele   +2 more
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A Prime Ideal Principle in commutative algebra

Journal of Algebra, 2008
In this paper, we offer a general Prime Ideal Principle for proving that certain ideals in a commutative ring are prime. This leads to a direct and uniform treatment of a number of standard results on prime ideals in commutative algebra, due to Krull ...
T Y Lam, Manuel L Reyes
exaly   +2 more sources

pm-Rings and the Prime Ideal Theorem

Topology and Its Applications, 2011
A commutative ring A with unit is called a pm-ring if every prime ideal of A is contained in a unique maximal ideal, and a Gelfand ring if a+b=1 in A implies that (1+ar)(1+bs)=0 for some r,s∈A. It was shown earlier, in a somewhat circuitous way involving
Bernhard Banaschewski
exaly   +2 more sources

A note On 2-prime ideals [PDF]

Journal of Mahani Mathematical Research
Let $R$ be a commutative ring with identity. In this paper, we study 2-prime ideals of a Dedekind domain and a Pr\"{u}fer domain. We prove that a nonzero ideal $I$ of a Dedekind domain $R$ is 2-prime if and only if $I=P^{\alpha}$, for some maximal ideal $
Somayeh Hadjirezaei, Vajihe Sharifi
doaj   +3 more sources