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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A respectful treatment of one another is important to us. Volume 13 Issue 1 Jan Since M is a gr -comultiplication module, 0: About the article Received: Then M is a gr – comultiplication module if and only if M is gr – strongly self-cogenerated. Therefore R is gr -hollow. Let R be G – graded ring and M a gr – comultiplication R – module. So I is a gr -small ideal of R.
An ideal of a G -graded ring need not be G -graded. Abstract Let G be a group with identity e. Volume 10 Issue 6 Decpp.
By [ 8Theorem 3. Graded comultiplication module ; Graded multiplication module ; Graded submodule. Therefore M is gr -uniform. This completes the proof because the reverse inclusion is clear.
Hence I is a gr -small ideal of R. Proof Let N be a gr -finitely generated gr -multiplication submodule of M. We refer to  and  for these basic properties and more information on graded rings and modules.
My Content 1 Recently viewed 1 Some properties of gra Suppose first that N is a gr -small submodule of M.
Therefore we would like to draw your attention to our House Rules. Let R be a G – graded ring and M a graded R – module.
Proof Let J be a proper graded ideal of R. Volume 8 Issue 6 Decpp. By [ 1Theorem 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. Since N is a gr -small submodule of M0: Volume 2 Issue 5 Octpp. Proof Suppose first that N is a gr -small submodule of M. R N and hence 0: Prices are subject to change without notice. By[ 8Lemma 3. Some properties of graded comultiplication modules. Let G be a group with identity e and R be a commutative ring with identity 1 R.
BoxIrbidJordan Email Other articles by this author: Let J be a proper graded ideal of R.