Prime Submodules and Local Gabriel Correspondence in σ[M]
JC Pérez, JR Montes - Communications in Algebra, 2012 - Taylor & Francis
JC Pérez, JR Montes
Communications in Algebra, 2012•Taylor & FrancisWe consider the concept of prime submodule defined by Raggi et al.. We find equivalent
conditions for a module M progenerator in σ [M], with τ M-Gabriel dimension, to have a one-
to-one correspondence between the set of isomorphism classes of indecomposable τ-
torsion free injective modules in σ [M] and the set of τ-pure submodules prime in M, where τ
is a hereditary torsion theory in σ [M]. Also we give a relation between the concept of prime
M-ideal given by Beachy and the concept of prime submodule in M. We obtain that if M is …
conditions for a module M progenerator in σ [M], with τ M-Gabriel dimension, to have a one-
to-one correspondence between the set of isomorphism classes of indecomposable τ-
torsion free injective modules in σ [M] and the set of τ-pure submodules prime in M, where τ
is a hereditary torsion theory in σ [M]. Also we give a relation between the concept of prime
M-ideal given by Beachy and the concept of prime submodule in M. We obtain that if M is …
We consider the concept of prime submodule defined by Raggi et al. . We find equivalent conditions for a module M progenerator in σ[M], with τ M -Gabriel dimension, to have a one-to-one correspondence between the set of isomorphism classes of indecomposable τ-torsion free injective modules in σ[M] and the set of τ-pure submodules prime in M, where τ is a hereditary torsion theory in σ[M]. Also we give a relation between the concept of prime M-ideal given by Beachy and the concept of prime submodule in M. We obtain that if M is progenerator in σ[M], then these concepts are equivalent.
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