Free 3-Generated Lattices with Two Semi-Normal Generators

We consider a lattice generated by three elements, two of which are semi-normal. We have proved it is infinite and have also found an additional condition for the lattice to be modular. As a result, it is proved that the sublattice generated in the subgroup lattice by two normal subgroups and any subgroup is modular.     

Finiteness and Infiniteness of 3-Generated Lattices with Distributive Elements Among Generators

Siberian Mathematical Journal - We consider 3-generated lattices whose generators are distributive, dually distributive, right modular, dually right modular elements, or elements possessing a...     

(2, 3)-Generated Groups with Small Element Orders

Algebra and Logic - A periodic group is called an OCn-group if the set of its element orders consists of all natural numbers from 1 to some natural n. W. Shi posed the question whether every...     

Chains of Modular Elements and Lattice Connectivity

We show that the order complex of any finite lattice with a chain of modular elements is at least (r−2)-connected. The first author was supported during part of this work by a postdoctoral fellowship from the Mathematical Sciences Research Institute. The second author was supported by NSF grant DMS-0300483.     

Modular Lattice for C 0-Operators

We prove modularity of the lattice Lat (T) of closed invariant subspaces for a C ₀-operator T with property (P). To my parents     

The Comparability Graph of a Modular Lattice

L of rank is d-connected if there exists a closed interval of rank 3 of L with , where is the M?bius function of L. Received: January 18, 1996     

正交模格OML上的同余关系

介绍了正交模格上同余关系的性质,给出正交模格上一个二元关系是同余关系的条件.证明了正交模格上的理想是正交模理想的充分必要条件扣等价命题,最后介绍了换位子理想.     

弱P-正则半群上的幂等元分离同余格

在本文中，弱P-正则半群上的弱P-正则，弱正规子集的概念被介绍．在弱P-正则半群上的弱P-正则，弱正规子集的若干性质被获得后，我们给出了弱P-正则半群上的幂等元分离同余格的一个刻画。     

On Locally Finite Modular Lattice Varieties of Finite Height

It is shown that the variety generated by a finite modular lattice has only finitely many locally finite covers.      

格蕴涵代数的左幂等元

为了研究命题真值取于格上的逻辑系统,文献[1]给出了格蕴涵供数的概念,文献[2-6]给出了格蕴涵代数的滤子,同态和性质（P）的概念,并讨论了它们的一些性质。本文在格蕴函代数中引入左幂等元的概念,讨论格蕴函代数中左幂等元的性质及由全体左幂等元所构成集合的代数结构,得到格蕴涵代数的分解定理：格蕴涵代数可以分解为由左幂等元构成左映射的像集合与对偶核的直和。     

Separating Maps of the Lattice E 8 and Triangulations of the Eight-Dimensional Torus

Our goal is to build triangulations of the eight-dimensional torus with 511 vertices, 511 being the smallest number of vertices of the known triangulations of the torus. We define the separating maps from the lattice E ₈ to Z / 511 Z and we establish the list of such maps up to symmetry. Received February 26, 1999, and in revised form June 9, 1999.     

The Steinberg Lattice of a Finite Chevalley Group and its Modular Reduction

Let p be a prime and let q = p^a, where a is a positive integer.Let G 7equals; G(F_q) be a Chevalley group over F_q, with associatedsystem of roots and Weyl group W. Steinberg showed in 1957that G has an irreducible complex representation whose degreeequals the p-part of |G| [11]. This representation, now knownas the Steinberg representation, has remarkable properties,which reflect the structure of G, and there have been many researchpapers devoted to its study. The module constructed in [11]is in fact a right ideal in the integral group ring ZG of G,and is thus a ZG-lattice, which we propose to call the Steinberglattice of G. It should be noted that lattices not integrallyisomorphic to the Steinberg lattice may also afford the Steinbergrepresentation, and such lattices may differ considerably intheir properties compared with the Steinberg lattice.     

Stabilizability and Semigroups with Discrete Generators

A number of semigroups of bounded linear transformations ona Banach space of importance in applications have the propertythat the infinitesimal generator is "discrete". For evolutionequations defined through such semigroups, it is often possibleto give simple criteria for stabilizability (and detectability).Such criteria are important in the study of certain controland filtering problems.     

Generators of matrix algebras in dimension 2 and 3

Let K be an algebraically closed field of characteristic zero and consider a set of 2×2 or 3×3 matrices. Using a theorem of Shemesh, we give conditions for when the matrices in the set generate the full matrix algebra.     

分离向量,分离泛函与自反性

本文利用严格分离向量和严格分离泛函讨论了算子子空间的自反性及遗传自反性