Results 11 to 20 of about 1,745,236 (282)
Journal of Applied Mathematics, 2013 We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that .
Areej M. Abduldaim, Sheng Chen
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Strongly regular modules [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2023 Summary: The notion of strongly regular modules over a ring which is not necessarily commutative is introduced. The relation between \(F\)-regular, \(GF\)-regular and \(vn\)-regular modules that are defined over commutative rings and strongly regular module is obtained. We have shown that a remark that if \(R\) is a reduced ring, then the \(R\)-module \
Govindarajulu Narayanan Sudharshana +1 more
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The Unique Maximal GF-Regular Submodule of a Module
The Scientific World Journal, 2013 An R-module A is called GF-regular if, for each a∈A and r∈R, there exist t∈R and a positive integer n such that rntrna=rna. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by MGF(A).
Areej M. Abduldaim, Sheng Chen
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Glasgow Mathematical Journal, 2017 AbstractIn 2014, the first two authors proved an extension to modules of a theorem of Camillo and Yu that an exchange ring has stable range 1 if and only if every regular element is unit-regular. Here, we give a Morita context version of a stronger theorem.
Chen, H., Nicholson, W. K., Zhou, Y.
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New Concepts on Module Arens Regularity for Module Banach Algebras
Journal of MathematicsThe main purpose of this paper is to introduce a new definition of JA-module Arens regularity, which extends former standard definition. Then a new module structure on the semigroup algebra l1S as l1ES-module with nontrivial right and left module actions
Omid Pourbahri Rahpeyma +2 more
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The Jacobson Radical and Regular Modules
Canadian Mathematical Bulletin, 1975 Let A be an associative, but not necessarily commutative, ring with identity, and J = J(A) its Jacobson radical. A (unital) module is regular iff every submodule is pure (see (1)). The regular socle R(M) of a module M is the sum of all its submodules which are regular. These concepts have been introduced and studied in (2).
David J. Fieldhouse
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Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017 In this paper we introduced the concept of 2-pure submodules as a generalization of pure submodules, we study some of its basic properties and by using this concept we define the class of 2-regular modules, where an R-module M is called 2-regular ...
Nuhad S. AL-Mothafar, Ghaleb A. Humod
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Characterizations of rings and modules by means of lattices [PDF]
, 1965 PhDIn this thesis we study the relationship between the lattice of submodules and the algebraic structure of a module. The key remark in our study will be the fact that the homomorphisms between two independent submadules of a module can be ...
Stephenson, W.
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Permutation module decomposition of the second cohomology of a regular semisimple Hessenberg variety [PDF]
, 2022 Regular semisimple Hessenberg varieties admit actions of associated Weyl groups on their cohomology space of each degree. In this paper, we consider the module structure of the cohomology spaces of regular semisimple Hessenberg varieties of type $A$.
Cho, Soojin +2 more
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Regular and semisimple modules [PDF]
Pacific Journal of Mathematics, 1976 is a T-ring.(1)—>(3b). A semisimple module is torsion.(3)—>(1). This is an immediate consequence of Lemma 4.Neither (3a) nor (3b) is sufficient by itself to imply (1). TomShorem has shown (unpublished) that the product of an infinitenumber of fields (or an infinite number of copies of a single field)is a T-ring. Thus (3a) does not imply (1).
Cheatham, T. J., Smith, J. R.
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