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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Let R be a G – graded ring and M a gr – comultiplication R – kodules. Suppose first that M is gr -comultiplication R -module and N a graded submodule of M.
My Content 1 Recently viewed 1 Some properties of gra Let R be G – graded ring and M a gr – comultiplication R – module. Volume 14 Issue 1 Janpp. Conversely, let N be a graded submodule of M. Proof Let N be a gr -finitely generated gr -multiplication submodule of M. Volume 15 Issue 1 Janpp.
Mathematics > Commutative Algebra
Let N be a gr -finitely generated gr -multiplication submodule of M. Thus by [ 8Lemma 3. Here we will study the class of graded comultiplication modules and obtain some further results which are dual to classical results on graded multiplication modules see Section 2. Volume 12 Issue 12 Decpp. Let R be a G – graded ringM a gr – comultiplication R – module and 0: A graded R -module M is said to be gr – uniform resp.
Let R be a G -graded commutative ring and M a graded R -module.
Some properties of graded comultiplication modules : Open Mathematics
Recall that a G -graded ring R is said to be a gr -comultiplication ring if it is a gr -comultiplication R -module see . Some properties of graded comultiplication modules. Then M is gr – hollow module. Let G be a group with identity e and R be a commutative moduels with identity 1 R. BoxIrbidJordan Email Other articles by this author: In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.
Volume 11 Issue 12 Decpp. As a dual concept of gr -multiplication modules, graded comultiplication modules gr -comultiplication modules were introduced and studied by Ansari-Toroghy and Farshadifar . User Account Log in Register Help.
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It follows that M is gr -hollow module. Prices are subject to change without notice. Let G be a group with identity e. Volume 2 Issue 5 Octpp.
Therefore M is gr -uniform. If M is a gr – comultiplication gr – prime R – modulethen M is a gr – simple module.
Volume 5 Issue 4 Decpp. Since N is a gr -small submodule of M0: Since M is gr -uniform, 0: Suppose first that N is a gr -small submodule of M.
An ideal of a G -graded ring need not be G -graded. Let R be a G – graded ring and M a graded R – module.