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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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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
Idempotent monads and . . .
"... For an associative ring R, let P be an Rmodule with S = EndR(P). C. Menini and A. Orsatti posed the question of when the related functor HomR(P, −) (with left adjoint P ⊗S −) induces an equivalence between a subcategory of RM closed under factor modules and a subcategory of SM closed under submod ..."
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submodules. They observed that this is precisely the case if the unit of the adjunction is an epimorphism and the counit is a monomorphism. A module P inducing these properties is called a ⋆module. The purpose of this paper is to consider the corresponding question for a functor G: B → A between arbitrary
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
Idempotent Monads and *Functors
, 2009
"... For an associative ring R, let P be an Rmodule with S = EndR(P). C. Menini and A. Orsatti posed the question of when the related functor HomR(P, −) (with left adjoint P ⊗S −) induces an equivalence between a subcategory of RM closed under factor modules and a subcategory of SM closed under submodu ..."
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Cited by 3 (3 self)
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submodules. They observed that this is precisely the case if the unit of the adjunction is an epimorphism and the counit is a monomorphism. A module P inducing these properties is called a ⋆module. The purpose of this paper is to consider the corresponding question for a functor G: B → A between arbitrary
ON RADICALS OF MODULE COALGEBRAS
, 2006
"... Abstract. We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of Bmodule coalgebras, then every Bmodule coalgebra contains a unique maximal Bsubmodule coalgebra in R. Moreover, a Bmodule coalgebra C is a m ..."
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Cited by 3 (1 self)
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Abstract. We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of Bmodule coalgebras, then every Bmodule coalgebra contains a unique maximal Bsubmodule coalgebra in R. Moreover, a Bmodule coalgebra C is a
Journal of Pure and Applied Algebra 212 (2008) 157–167 www.elsevier.com/locate/jpaa On radicals of module coalgebras
, 2007
"... Communicated by C. Kassel We introduce the notion of an idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of Bmodule coalgebras, then every Bmodule coalgebra contains a unique maximal Bsubmodule coalgebra in R. Moreover, a Bmodule ..."
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Communicated by C. Kassel We introduce the notion of an idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of Bmodule coalgebras, then every Bmodule coalgebra contains a unique maximal Bsubmodule coalgebra in R. Moreover, a B
Czechoslovak Mathematical Journal, 58 (133) (2008), 381–393 EXTENDING MODULES RELATIVE TO A TORSION THEORY
, 2006
"... Abstract. An Rmodule M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τextending module, where τ is a hereditary torsion theory on ModR. An Rmodule M is called type 2 τextending if every ty ..."
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type 2 τclosed submodule of M is a direct summand of M. If τI is the torsion theory on ModR corresponding to an idempotent ideal I of R and M is a type 2 τIextending Rmodule, then the question of whether or not M/MI is an extending R/Imodule is investigated. In particular, for the Goldie torsion
ON THE ENDOMORPHISM RING OF A SEMIINJECTIVE MODULE
"... Abstract. Let R be a ring. A right Rmodule M is called quasiprincipally (or semi) injective if it is Mprincipally injective. In this paper, we show: (1) The following are equivalent for a projective module M: (a) Every Mcyclic submodule of M is projective; (b) Every factor module of an Mprinci ..."
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Cited by 6 (3 self)
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Abstract. Let R be a ring. A right Rmodule M is called quasiprincipally (or semi) injective if it is Mprincipally injective. In this paper, we show: (1) The following are equivalent for a projective module M: (a) Every Mcyclic submodule of M is projective; (b) Every factor module of an M
Results 1  10
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