# COMULTIPLICATION MODULES PDF

H Ansari-Toroghy, F FarshadifarOn comultiplication modules. Korean Ann Math, 25 (2) (), pp. 5. H Ansari-Toroghy, F FarshadifarComultiplication. Key Words and Phrases: Multiplication modules, Comultiplication modules. 1. Introduction. Throughout this paper, R will denote a commutative ring with identity . PDF | Let R be a commutative ring with identity. A unital R-module M is a comultiplication module provided for each submodule N of M there exists an ideal A of.

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Volume 4 Issue 4 Dec comultiplidation, pp. Since N is a gr -small submodule of M0: A graded R -module M is said to be gr – uniform resp. Then M is a gr – comultiplication module if and only if M is gr – strongly self-cogenerated. Then the following hold: Let R be a G -graded ring and M an R -module.

### Some properties of graded comultiplication modules : Open Mathematics

Let R be a G -graded commutative ring and M a graded R -module. A graded R -module M is said to be gr – simple if 0 and M are its only graded mldules.

Proof Suppose first that N is a gr -small submodule of M. Suppose first that M is gr -comultiplication R -module and N a graded submodule of M.

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Suppose first that N is a gr -small submodule of M. Abstract Let G be a group with identity e. My Content 1 Recently viewed 1 Some properties of gra Let R be G – graded ring and M a gr – comultiplication R – module.

Proof Let Cmoultiplication be a gr -finitely generated gr -multiplication submodule of M. Since M is a gr -comultiplication module, 0: Graded multiplication modules gr -multiplication modules over commutative graded ring have been studied by many authors extensively see [ 1 — 7 ].

Let G be a group with identity e.

## Mathematics > Commutative Algebra

Therefore M is a gr -simple module. Prices do not include postage and handling if applicable. Volume 8 Issue 6 Decpp.

Since M is gr -uniform, 0: Recall that a G -graded ring R is said to be a gr -comultiplication ring if it is a gr -comultiplication Comultiplicqtion -module see [8]. Let R be a G-graded ring and M a graded R – module. Volume 7 Issue 4 Decpp.

### [] The large sum graph related to comultiplication modules

See all formats and pricing Online. An ideal of a G -graded ring need not be G -graded. Volume 3 Issue 4 Decpp. Therefore R is gr -hollow. Let R be a G – graded ring and M a gr – faithful gr – comultiplication module with the property 0: About the article Received: Proof Note first that K: A respectful treatment of one another is important to us. User Account Log in Register Help. Since N is a gr -large submodule of M0: Volume 14 Issue 1 Janpp.

Therefore M is a gr -comultiplication module.