The following sections are included:Support of a moduleAssociated prime idealsDimension of a moduleDepth of a moduleCohen–Macaulay modulesModules of finite projective dimensionThe Koszul complexRegular local ringsProjective dimension and depthℑ-depthThe acyclicity theoremAn example Support of a module ...
Introduction In this discussion every module over a ring R will be understood to be a left i2-module. R will always have a unit, and every module will be unitary. The aim of this paper is to study the structure and properties of injective modules, particularly over Noetherian DOI: 10.2140...
Let R be a commutative ring with unity, M a module over R and let S be a G-set for a finite group G. We define a set MS to be the set of elements expressed as the formal finite sum of the form similar to the elements of group ring RG. The set MS is a module over the gro...
The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free ...
A right module M over a ring R is called small dual-ADS, if for each decomposition M=A⊕B, then A and B are mutually small projective. Small dual-ADS modules are the dual analogue of LADS modules, a class of modules recently studied. In this article, we study several properties of ...
All finitely generated right A -modules are ℵ 0 -injective if and only if A is a regular, right ℵ 0 -injective ring.
Let R-Mod be the category of unital left modules over a ring R. It is shown that a finitely closed subcategory K of R-Mod is an AB5∗ category if and only if K is dual to some finitely closed subcategory of Mod-T, for a suitable ring T. From this it follows that, for any...
The work is carried out over the category of right A -modules; where A is an arbitrary ring, which is always associative and possesses identity. Accordingly, this work is based on a type of module called "static module related to a fixed A -moduleM or "M- static A -module. The main...
Module over finite chain ringGraded posetWhitney numbersAntichainSperner’s theoremWe prove Sperner-type theorems for the partially ordered setPM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\use...
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