let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

the largest class of algebraic hyper structures satisfying the module like axioms is the v h -module. in this paper, we consider the category of v h -modules and prove that the direct limit alwaysexists in this category. direct limits are defined by a universal property, and so are unique. the mostpowerful tool in order to obtain a module from a given v h - module is the quotient out procedure....

upTEX is a Unicode extension of ASCII’s pTEX (a Japanese-localized TEX). It not only improves Japanese support, but also handles Chinese and Korean characters, i.e., Kanji (Hanzi, Hanja), Kana, CJK symbols, and Hangul with Unicode. Moreover, it can process multilingual typesetting of original LTEX with inputenc and Babel (Latin, Cyrillic, Greek, etc.) by switching its \kcatcode tables. This pap...

Many textbook proofs are essentially human-readable representations of natural deduction proofs. Terms in dependent type theory provide formally checkable representations of natural deduction proofs. We show how the new mathematical assistant system Scunak can be used to verify a textbook proof by translating the LTEX version into a proof term in a dependent type theory. We also show how Scunak...

In this paper Bibulus will be introduced. Bibulus is a very flexible, multilingual system for formatting bibliographies in several formats, including LTEX. Bibliographies are stored in XML, but Bibulus includes a program to convert old BTEX databases. Bibulus is being developed as open-source software at http://savannah.nongnu.org/ projects/bibulus/. This paper will first summarise the curren...

ABSTRACT A brief summary at the beginning highlights the major points of your paper. Include the complete names of all SAS R © (First use of company name SAS must have R ©.) products that are discussed in the paper, names of operating environments (if applicable), and the skill level that the intended audience should have. (9-point Arial regular) Note: sugconf.cls uses Adobe Helvetica san-serif...

Common Lisp Quick Reference Revision 134 [2012-04-05] Copyright © 2008, 2009, 2010, 2011, 2012 Bert Burgemeister LTEX source: http://clqr.boundp.org Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no FrontCover Texts...

In the present paper for two $mathfrak{A}$-module Banach algebras $A$ and $B$, we investigate relations between $varphi$-$mathfrak{A}$-module approximate amenability of $A$, $psi$-$mathfrak{A}$-module approximate amenability of $B$, and $varphioplus psi$-$mathfrak{A}$-module approximate amenability of $Aoplus B$ ($l^1$-direct sum of $A$ and $B$), where $varphiin$ Hom$_{mathfrak{A}}(A)$ and $psi...

in this paper we introduce a generalization of m-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . we will use the structure of the radical of a module in  and get some suitable results about this class of modules. also the relation between injective hull in  and this kind of modules will be investigated in this article.   for a module  we show...