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Pure Submodules of Multiplication Modules
"... Abstract. The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and ..."
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Cited by 3 (1 self)
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Abstract. The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication
sPURE SUBMODULES
, 2005
"... A submodule A of a right Rmodule B is called spure if f ⊗R 1S is a monomorphism for every simple left Rmodule S,where f: A → B is the inclusion homomorphism. We establish some properties of spure submodules and use spurity to characterize commutative rings with every maximal ideal idempotent. 1 ..."
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A submodule A of a right Rmodule B is called spure if f ⊗R 1S is a monomorphism for every simple left Rmodule S,where f: A → B is the inclusion homomorphism. We establish some properties of spure submodules and use spurity to characterize commutative rings with every maximal ideal idempotent
sPURE SUBMODULES
, 2005
"... A submodule A of a right Rmodule B is called spure if f ⊗R 1S is a monomorphism for every simple left Rmodule S, where f: A → B is the inclusion homomorphism.We establish some properties of spure submodules and use spurity to characterize commutative rings with every maximal ideal idempotent. ..."
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A submodule A of a right Rmodule B is called spure if f ⊗R 1S is a monomorphism for every simple left Rmodule S, where f: A → B is the inclusion homomorphism.We establish some properties of spure submodules and use spurity to characterize commutative rings with every maximal ideal idempotent
sPURE SUBMODULES
, 2005
"... A submodule A of a right Rmodule B is called spure if f ⊗R 1S is a monomorphism for every simple left Rmodule S, where f: A → B is the inclusion homomorphism.We establish some properties of spure submodules and use spurity to characterize commutative rings with every maximal ideal idempotent. ..."
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A submodule A of a right Rmodule B is called spure if f ⊗R 1S is a monomorphism for every simple left Rmodule S, where f: A → B is the inclusion homomorphism.We establish some properties of spure submodules and use spurity to characterize commutative rings with every maximal ideal idempotent
WEAKLY PURE SUBMODULES OF MULTIPLICATION MODULES
, 2010
"... Abstract Let R be a commutative ring with nonzero identity and M be a unital Rmodule. This paper is devoted to investigate some of the properties of weakly pure submodules of multiplication modules. ..."
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Abstract Let R be a commutative ring with nonzero identity and M be a unital Rmodule. This paper is devoted to investigate some of the properties of weakly pure submodules of multiplication modules.
© Hindawi Publishing Corp. ON QUASI hPURE SUBMODULES OF QTAGMODULES
, 1999
"... Abstract. Different concepts and decomposition theorems have been done for QTAGmodules by number of authors. We introduce quasi hpure submodules for QTAGmodules andwe obtain several characterizations for quasihpure submodules and as a consequence we deduce a result done by Fuchs 1973. ..."
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Abstract. Different concepts and decomposition theorems have been done for QTAGmodules by number of authors. We introduce quasi hpure submodules for QTAGmodules andwe obtain several characterizations for quasihpure submodules and as a consequence we deduce a result done by Fuchs 1973.
Weakly Pure and Weakly Copure Submodule of Multiplication Modules
"... ABSTRACT: In this paper we introduce weakly copure submodule of multiplication module which is dual notion of weakly pure submodule of multiplication module and investigate some properties of weakly pure and copure submodule of multiplication module. ..."
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ABSTRACT: In this paper we introduce weakly copure submodule of multiplication module which is dual notion of weakly pure submodule of multiplication module and investigate some properties of weakly pure and copure submodule of multiplication module.
On unitarily equivalent submodules
 MR2482998 (2010d:46031), Zbl 1172.46015
"... Abstract. The Hardy space on the unit ball in Cn provides examples of a quasifree, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for m ..."
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Cited by 7 (7 self)
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Abstract. The Hardy space on the unit ball in Cn provides examples of a quasifree, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur
Some Characterizations of Submodules of QT AGMODULES a
"... Abstract. A module M over an associative ring with unity is a QT AGmodule if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. There are many fascinating concepts related to these modules of which hpure submodules and Nhigh submodules are very ..."
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Abstract. A module M over an associative ring with unity is a QT AGmodule if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. There are many fascinating concepts related to these modules of which hpure submodules and Nhigh submodules are very
Results 1  10
of
55