Kleene代数的诱导子代数及理想

由于逻辑学研究的需要 ,Kleene代数理论的重要性已越来越明显 .本文主要研究了Kleene代数的子代数及理想的一些性质 ,得到了一些比较好的结果 .     

Ideals and congruences in effect algebras and qmv-algebras

Ideals and sets of ideals of different types on QMV-algebras and the corresponding effect algebras are studied and compared.     

半群上的粗糙理想的性质

给出二型理想(two-type ideal)的概念，讨论它的一些性质，及与理想相联系的格林等价关系(Green’s equivalence relations)下的各种理想的逼近(approximation)问题。     

BCI代数的软关联理想和软正定关联理想

给出BCI代数的软关联理想和软正定关联理想的概念,讨论软理想、软关联理想和软正定关联理想三者之间的关系,研究了两个软关联理想(软正定关联理想)的扩展交、限制交、限制并和限制差分的性质。     

Obstructions to Compatible Splittings

Suppose one has a map of split short exact sequences in a category of modules, or more generally, in any abelian category. Do the short exact sequences split compatibly, i.e., does there exist a splitting of each short exact sequence which commutes with the map of short exact sequences? The answer is sometimes “yes” and sometimes “no”. We define and prove basic properties of a group of obstructions to the existence of compatible splittings.     

半群中的粗糙模糊理想及粗糙模糊素理想

将粗糙集的理论方法用于模糊半群的研究。给出上(下)粗模糊子半群及上(下)粗模糊左(右)理想、粗糙模糊素理想等概念,研究它们的有关性质。证明上粗模糊子半群与上粗模糊理想是通常的模糊子半群与模糊理想概念的扩张。     

BCH-代数的拟结合理想和拟结合模糊理想

在BCH-代数中,引入了拟结合理想和模糊拟结合理想的概念.研究了BCH-代数中模糊拟结合理想的相关性质,给出了BCH-代数拟结合理想的构造.     

半群的模糊理想及生成模糊理想

研究半群的模糊理想,利用λ-截集、确界原理对半群的模糊理想作进一步讨论,给出生成模糊理想的构造.     

模糊(左,右)理想格的结构

本文利用截集和集合套理论研究模糊（左,右）理想格的结构。证明了环Ｒ的模糊（左,右）理想格是模格,并给出了这类格中并ＨＶＫ的构造。     

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。     

Ideals in the Roe Algebras of Discrete Metric Spaces with Coefficients in B（H）

The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu＇s property A, the ideal structure of the Roe algebra of X with coefficients in B（H） is completely characterized by the ideal families of weighted subspaces of X, where B（H） denotes the C＊-algebra of bounded linear operators on a separable Hilbert space H.     

Ideals in the Roe Algebras of Discrete Metric Spaces with Coefficients in B(H)

The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced.It is shown that,if X has Yu's property A,the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X,where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.     

近环的理想与导子

设Ｎ是中心为Ｚ的素近环,Ｉ是Ｎ的右理想,Ｄ是Ｎ上的非平凡导子,本文证明了１）若Ｄ（Ｉ）∈Ｚ,则（Ｎ１＋）是交换的;又若Ｎ２－挠自由,则Ｎ是无零因子交换环,（２）若０≠Ｄ＾ｎ（Ｉ）∈Ｚ,Ｄ＾ｎ－１（Ｉ）∈Ｉ,且Ｎ是（ｎ＋１）１挠自由的,则Ｎ是无零因子交换环。     

Koszul Algebras and Their Ideals

We study associative graded algebras that have a “complete flag” of cyclic modules with linear free resolutions, i.e., algebras over which there exist cyclic Koszul modules with any possible number of relations (from zero to the number of generators of the algebra). Commutative algebras with this property were studied in several papers by Conca and others. Here we present a noncommutative version of their construction.We introduce and study the notion of Koszul filtration in a noncommutative algebra and examine its connections with Koszul algebras and algebras with quadratic Grobner bases. We consider several examples, including monomial algebras, initially Koszul algebras, generic algebras, and algebras with one quadratic relation. It is shown that every algebra with a Koszul filtration has a rational Hilbert series.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 47–60, 2005Original Russian Text Copyright © by D. I. PiontkovskiiSupported in part by the Russian Foundation for Basis Research under project 02-01-00468.     

Ideals in Morita Rings and Morita Semigroups

We characterize the lattice of all ideals of a Morita ring （semigroup） when the corresponding pair of rings （semigroups） in the Morita context are Morita equivalent s-unital （like-unitv） rings （semigroups）.     

布尔代数的Fuzzy子代数和Fuzzy理想

引入了布尔代数的Fuzzy子代数、Fuzzy理想和Fuzzy商布尔代数的概念,给出了布尔代数的Fuzzy集是Fuzzy子代数(Fuzzy理想)的充要条件,讨论了布尔代数的Fuzzy子代数(Fuzzy理想)在布尔代数同态下的像和逆像,得到了布尔代数的Fuzzy子代数的同态基本定理。     

BCH-代数的模糊理想与模糊H-理想

在BCK／BCI／BCC代数中Fuzzy理想被广泛研究，但在BCH-代数中还没有讨论过。在BCH-代数中引人了Fuzzy理想与FuzzyH-理想的概念，并讨论它们的性质。     

Borel Subalgebras Redux with Examples from Algebraic and Quantum Groups

Both building upon and revising previous literature, this paper formulates the general notion of a Borel subalgebra B of a quasi-hereditary algebra A. We present various general constructions of Borel subalgebras, establish a triangular factorization of A, and relate the concept to graded Kazhdan–Lusztig theories in the sense of Cline et al. (Tôhoku Math. J. 45 (1993), 511–534). Various interesting types of Borel subalgebras arise naturally in different contexts. For example, `excellent" Borel subalgebras come about by abstracting the theory of Schubert varieties. Numerous examples from algebraic groups, q-Schur algebras, and quantum groups are considered in detail.     

Ideals of smooth functions and residue currents

Let be a holomorphic mapping in a neighborhood of the origin in . We find sufficient condition, in terms of residue currents, for a smooth function to belong to the ideal in C^∞ (or C^k) generated by f. If f is a complete intersection the condition is necessary. More generally we give a sufficient condition for an element of class C^∞ (or C^k) in the Koszul complex induced by f to be exact. For the proofs we introduce explicit homotopy formulas for the Koszul complex induced by f.