ON ALMOST PRIME SUBMODULES

In this article,we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity.We study some basic properties of...     

Prime Submodules and Flat Modules

In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.     

Fuzzy蕴涵代数的素MP滤子

对Fuzzy蕴涵代数(简称FI代数)的滤子理论作深入研究.首先对由非空集合生成的MP滤子的性质作进一步探讨;然后引入素MP滤子的概念并讨论其基本性质,给出了素MP滤子的若干等价刻画,证明了并半格FI代数的素MP滤子定理;最后利用素MP滤子概念时满足条件(S)的并半格FI代数的MP滤子格((L)MP(X),(∩))中的素元进行刻画.     

A Note on Rings and Modules Graded by Some Special Groups

In this note we prove that the prime madicals of some graded rings and the scoles of some graded modules are also graded. The results on the relations between the prime radical and the graded prime radical are also presented. Moreover, the relations between a graded ring and its initial subring are studied.     

TL-子环和TL-理想--第5篇:素TL-理想和半素TL-理想

引入环的素ＴＬ－理想,全素ＴＬ－理想和半素ＴＬ－理想等概念,并且介绍了它们的一些基本性质,其中Ｔ为任意给定的完备Ｂｒｏｕｗｅｒ格Ｌ上的任意无穷并－分配ｔ－模。此外,还对有单位元的交换环的素ＴＬ－理想和一般的素（全素）ＴＬ－理想的特点进行刻划。     

半环上的模糊素理想和模糊素根

引入了半环的模糊素理想的概念,给出了它的几种刻画方式,得到了它的一些性质;进一步定义了模糊素理想的模糊素根,获得了一些漂亮结果。     

R_0代数中素滤子的拓扑性质

首先讨论了R_0代数M中MP滤子、素滤子的基本性质,然后通过自然的方式在M的全体素滤子之集PF_(IL)(M)上构造拓扑,证明了PF_(IL)(M)是紧致的T_0空间.最后把PF_(IL)(M)上的拓扑限制在M的全体极大滤子之集MF_(IL)(M)上,得到MF_(IL)(M)是紧致的Hausdorff空间.     

Some properties of elements of the prime field

We obtain some properties of primitive roots in the groups of residue class modulo prime number, in particular, Fermat primes and Sophie Germain primes. We also obtain some formulas for computation of products of elements in some subsets of the prime field of positive characteristic.     

关于两个多元多项式互素问题

给出了两个二元多项式互素的充要条件 ,然后利用这个充要条件推出二元多项式互素的性质 ,最后给出一般的 n元多项式互素的充要条件 .     

Hyperbolic stochastic differential equations: Absolute continuity of the LKW of the solution at a fixed point

LetW be the Wiener process onT=[0, 1]². Consider the stochastic integral equation $$\begin{gathered} X_\zeta = x_0 + \int_{R_\zeta } {a_1 (\zeta \prime )X(s\prime ,dt\prime )ds\prime + } \int_{R_\zeta } {a_2 (\zeta \prime )X(ds\prime ,t\prime )dt\prime } \hfill \\ + \int_{R_\zeta } {a_3 (X_{\zeta \prime , } \zeta \prime )W(ds\prime ,dt\prime ) + } \int_{R_\zeta } {a_4 (X_{\zeta \prime , } \zeta \prime )ds\prime ,dt\prime ,} \hfill \\ \end{gathered} $$ whereR _ζ =(s, t) ∈ T, andx ₀ ∈ ?. Under some assumptions on the coefficients a_i, the existence and uniqueness of a solution for this stochastic integral equation is already known (see [6]). In this paper we present some sufficient conditions for the law ofX _ζ to have a density.     

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．     

Fuzzy prime filters of lattice implication algebras

In this paper, some properties of fuzzy filters are given. Besides, the structure of fuzzy filters are further studied. And finally, the concept of fuzzy prime filter is proposed with some equivalent conditions of fuzzy prime filters obtained.     

具有素中心环的若干性质(英文)

给出了素中心环的若干新的性质 ,在具有素中心的条件下 ,我们证明了 :环的幂零元与强幂零元是一致的 ;环的素根与诣零根是相同的 ;环的满自同态是自同构 ;对于每个 a∈ R,序列 Ra Ra2 …是稳定的当且仅当对于每个 a∈ R,存在自然数 n使得 an是一个正则元 .研究了某些具有素中心的特殊环     

Schönemann–Eisenstein–Dumas-Type Irreducibility Conditions that Use Arbitrarily Many Prime Numbers

The famous irreducibility criteria of Schönemann–Eisenstein and Dumas rely on information on the divisibility of the coefficients of a polynomial by a single prime number. In this paper, we will use some results and ideas of Dumas to provide several irreducibility criteria of Schönemann–Eisenstein–Dumas-type for polynomials with integer coefficients, criteria that are given by some divisibility conditions for their coefficients with respect to arbitrarily many prime numbers. A special attention will be paid to those irreducibility criteria that require information on the divisibility of the coefficients by two distinct prime numbers.     

Examples of prime Jordan superalgebras of vector type and superalgebras of Cheng-Kac type

We construct some examples of prime Jordan superalgebras of vector type whose odd part is a finitely generated projective module of rank 1 with arbitrarily many generators. These provide some examples of prime Jordan superalgebras of Cheng-Kac type.     

Spectral partially ordered sets

We examine some topics related to (gold)spectral partially ordered sets, i.e., those that are order isomorphic to (Goldman) prime spectra of commutative rings. Among other results, we characterize the partially ordered sets that are isomorphic to prime spectra of rings satisfying the descending chain condition on radical ideals, and we show that a dual of a tree is isomorphic to the Goldman prime spectrum of a ring if and only if every chain has an upper bound. We also give some new methods for constructing (gold)spectral partially ordered sets.     

偏序集中的弱理想和弱滤子

在偏序集上利用上集算子和下集算子引入了弱理想,弱滤子,弱素理想,弱素滤子,弱极大理想和弱极大滤子等概念,研究了它们的若干性质,同时给出了偏序集上的(DPI),(BPI),(DMI),(BUF)公理并建立了它们与Zorn引理之问的相互关系.     

Pseudocomplementation and minimal prime ideals in semirings

In Section 2 of the present paper, we introduce the concept of pseudocomplementation for semirings and show the semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some interesting results for minimal prime ideals of such semirings. In Section 3, some classical results for minimal prime ideals in ring theory are generalized in the context of semiring theory.     

Prime tight frames

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize all prime harmonic tight frames and use thischaracterization to suggest effective analysis and synthesis computation strategies for such frames. Finally, we describe all prime frames constructed from the spectral tetris method, and, as a byproduct, we obtain a characterization of when the spectral tetris construction works for redundancies below two.     

关于格序群的极大素子群

研究了格序群的极大素子群的性质以及由素子群根系确定的几种格序群类的结构。