Right Bézout ring with waist is a right Hermite ring

We study noncommutative rings in which the Jacobson radical contains a completely prime ideal. It is proved that a right Bézout ring in which the Jacobson radical contains a completely prime ideal is a right Hermite ring. We describe a new class of Bézout rings that are not elementary divisor rings.     

Fuzzy半群中的Fuzzy素理想

探讨Fuzzy半群中Fuzzy素理想,Fuzzy 完全理想与Fuzzy理想的根的一些代数性质,证明Fuzzy半群中每一个Fuzzy理想是Fuzzy完全半素理想当且仅当它可表为一族Fuzzy完全素理想之交。     

Prime Ideals in Near-Rings

An ideal I of a near-ring R is a type one prime ideal if whenever a Rb ? I, then a ∈ I or b ∈ I. This paper considers the interconnections between prime ideals and type one prime ideals in near-rings. It also develops properties of type one prime ideals, gives several examples illustrating where prime and type one prime are not equivalent, and investigates the properties of the type one prime radical. Several different types of conditions are given which guarantee that a prime ideal is type one. The class of all near-rings for which each prime ideal is type one is investigated and many examples of such near-rings are exhibited. Various localized distributivity conditions are found which are useful in establishing when prime ideals will be type one prime.     

On the Ascent of Properties Related to Unique Factorization Domains

In this article, we develop equivalent conditions for a certain class of monoidal transform to inherit either the property of being a completely integrally closed domain that satisfies the ascending chain condition on principal ideals, the property of being a Mori domain, the property of being a Krull domain, or the property of being a unique factorization domain, respectively. Such a class of monoidal transform is given in terms of an (analytically) independent set that forms a prime ideal in the base domain. Characterizations are provided illustrating the necessity of the “prime ideal” hypothesis when the base domain is a Noetherian unique factorization domain.     

半群的完全素和素模糊理想

通过由模糊点生成的模糊理想给出了半单半群的刻画。同时也刻画了两类半群：一类是所有模糊理想是素理想。另一类是所有模糊理想为安全素理想。     

半群的模糊拟对称理想和它的根

本文定义了半群的模糊拟对称理想,研究了它和模糊素理想、模糊完全素理想之间的关系,并研究了它的根的特征     

满足右零化子特殊升链条件的环

本文讨论了满足右零化子特殊升链条件的环的性质以及与左、右完备环，ＱＦ－环的关系；给出了满足右零化子特殊升链条件的环中素理想是完全素理想的条件，从而给出了Ｇｏｌｄｉｅ定理的一个应用．     

A NOTE ON THE g-PRIME RADICAL IN GAMMA RINGS

ABSTRACT

The g-prime radical of a Γ-ring M is equal to either the zero ideal or the prime radical of M. If the prime radical of M is a non-zero ideal, then the following three conditions are equivalent; (i) g-prime radical of M is equal to the prime radical of M; (ii) every g-prime ideal is a prime ideal; and (iii) every g-semiprime ideal is a semiprime ideal.     

半环上的素、半素、完全素、完全半素模糊理想

引出半环中模糊点生成的模糊理想的定义,讨论了它的一些性质,并用它刻画了半环中素、半素、完全素、完全半素模糊理想,最后讨论了这几类理想的关系。     

D-strong and almostD-strong near-rings

In this paper,D-strong and almostD-strong near-rings have been defined. It has been proved that ifR is aD-strongS-near ring, then prime ideals, strictly prime ideals and completely prime ideals coincide. Also ifR is aD-strong near-ring with identity, then every maximal right ideal becomes a maximal ideal and moreover every 2-primitive near-ring becomes a near-field. Several properties, chain conditions and structure theorems have also been discussed.Most of the parts of this paper are included in author's doctoral dissertation at Sukhadia University Udaipur (1983). The author expresses his gratitude to Dr.S. C. Choudhary for his kind guidance.     

Quantum solvable algebras. Ideals and representations at roots of 1

Let R be a quantum solvable algebra. It is proved that every prime ideal I of R which is stable with respect to the quantum adjoint action is completely prime, and Fract(R/I) is isomorphic to the skew field of fractions of an algebra of twisted polynomials. We study the correspondence between symplectic leaves and irreducible representations. A conjecture of De Concini-Kac-Procesi on the dimension of irreducible representations is proved for sufficiently large l.     

Prosolvable subgroups of free products of profinite groups

In this paper we establish several equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of prime power ideals to be a general ZPI-ring. Using these results, we establish some equivalent conditions for a commutative ring in which every principal ideal is a finite intersection of primary ideals to be a general ZPI-ring.     

The decision of prime and primary ideal

We give more efficient criteria to characterise prime ideal or primary ideal. Further, we obtain the necessary and sufficient conditions that an ideal is prime or primary in real field from the Gröbner bases directly.     

Prime ideals in nilpotent Iwasawa algebras

Let G be a nilpotent complete p-valued group of finite rank and let k be a field of characteristic p. We prove that every faithful prime ideal of the Iwasawa algebra kG is controlled by the centre of G, and use this to show that the prime spectrum of kG is a disjoint union of commutative strata. We also show that every prime ideal of kG is completely prime. The key ingredient in the proof is the construction of a non-commutative valuation on certain filtered simple Artinian rings.     

Virtual logarithms

The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.     

Compact operator semigroups applied to dynamical systems

A right chain ordered semigroup is an ordered semigroup whose right ideals form a chain. In this paper we study the ideal theory of right chain ordered semigroups in terms of prime ideals, completely prime ideals and prime segments, extending to these semigroups results on right chain semigroups proved in Ferrero et al. (J Algebra 292:574–584, 2005).     

幂格的素理想和素对偶理想

在文 [1 ]中 ,引入了幂格的概念 ,并讨论了其相关性质 .本文在此基础上 ,讨论格与其幂格的理想 ,对偶理想的关系 ,以及格与其幂络的素理想 ,素对偶理想的关系 .     

半环的理想与同余

引入半环的完全素理想的概念.利用这一概念,研究了半环的同余,分别给出了半环的子直积分解的若干结果和同余的一种刻画.     

关于完全C＊置换子群

设H≤G,称H为G的完全C＊置换子群,如果对G的任意素数幂阶子群K,恒有x∈（H,K〉,使得HKx=KxH．本文利用素数幂阶子群的完全C＊置换性给出了一个群属于给定群系的的若干充要条件．     

关于完全C~*置换子群

设H≤G,称H为G的完全C*置换子群,如果对G的任意素数幂阶子群K,恒有x∈〈H,K〉,使得HKx=KxH.本文利用素数幂阶子群的完全C*置换性给出了一个群属于给定群系的的若干充要条件.