General RM Rings
The concept of central RM rings is introduced in this paper as a generalization of RM rings. Since every RM ring is central RM we study the sufficient condition for a central RM ring to be a RM one. It is shown that every central reversible and hence every central symmetric is central RM ring, how...
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Refaad
2020-09-01
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| Series: | General Letters in Mathematics |
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| Online Access: | https://www.refaad.com/Files/GLM/GLM-9-1-3.pdf |
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doaj-db377e88ea3b4cc0a4b7a391a53626af2020-11-25T03:41:41ZengRefaadGeneral Letters in Mathematics 2519-92692519-92772020-09-0191173210.31559/glm2020.9.1.3General RM RingsChenar Abdul Kareem Ahmed0Department of Mathematics, University of Zakho, Kurdistan Region, IraqThe concept of central RM rings is introduced in this paper as a generalization of RM rings. Since every RM ring is central RM we study the sufficient condition for a central RM ring to be a RM one. It is shown that every central reversible and hence every central symmetric is central RM ring, however converse implications are wrong. It is also proven that the polynomial ring R[x] is central RM ring if R is central RM and quasi-Armendariz. Also α-RM ring has been studied with it is centralhttps://www.refaad.com/Files/GLM/GLM-9-1-3.pdfreflexive ringcentral reflexive ringmatrix ringα-rigid ringdorroh extension |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Chenar Abdul Kareem Ahmed |
| spellingShingle |
Chenar Abdul Kareem Ahmed General RM Rings General Letters in Mathematics reflexive ring central reflexive ring matrix ring α-rigid ring dorroh extension |
| author_facet |
Chenar Abdul Kareem Ahmed |
| author_sort |
Chenar Abdul Kareem Ahmed |
| title |
General RM Rings |
| title_short |
General RM Rings |
| title_full |
General RM Rings |
| title_fullStr |
General RM Rings |
| title_full_unstemmed |
General RM Rings |
| title_sort |
general rm rings |
| publisher |
Refaad |
| series |
General Letters in Mathematics |
| issn |
2519-9269 2519-9277 |
| publishDate |
2020-09-01 |
| description |
The concept of central RM rings is introduced in this paper as a generalization of RM rings. Since every RM ring is central
RM we study the sufficient condition for a central RM ring to be a RM one. It is shown that every central reversible and hence
every central symmetric is central RM ring, however converse implications are wrong. It is also proven that the polynomial ring
R[x] is central RM ring if R is central RM and quasi-Armendariz. Also α-RM ring has been studied with it is central |
| topic |
reflexive ring central reflexive ring matrix ring α-rigid ring dorroh extension |
| url |
https://www.refaad.com/Files/GLM/GLM-9-1-3.pdf |
| work_keys_str_mv |
AT chenarabdulkareemahmed generalrmrings |
| _version_ |
1724528902869614592 |