Strongly CM -semicommutative rings
Strongly CM -semicommutative rings
We study the strongly semicommutative properties relative to a monoid crossed product. The concept ofstrongly CM -semicommutative rings is introduced and investigated. Many results related to semicommutative propertiesover polynomial rings, skew polynomial rings, monoid rings, and skew monoid rings are extended and unified.
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- [1] Hashemi E, Moussavi A. Polynomial extensions of quasi-baer rings. Acta Math Hungar 2005; 107: 207-224.
- [2] Huh C, Lee Y, Smoktunowicz A. Armendariz rings and semicommutative rings. Comm Algebra 2002; 30: 751-761.
- [3] Kelarev AV. Ring Constructions and Applications. Singapore: World Scientific Publishing, 2002.
- [4] Kim NK, Lee Y. Armendariz rings and reduced rings. J Algebra 2000; 223: 477-488.
- [5] Kim NK, Lee Y. Extensions of reversible rings. J Pure Appl Algebra 2003; 185: 207-223.
- [6] Krempa J. Some examples of reduced rings. Algebra Colloq 1996; 3: 289-300.
- [7] Liu ZK. Armendariz rings relative to a monoid. Comm Algebra 2005; 33: 649-661.
- [8] Nagata M. Local Rings. New York, NY, USA: Interscience, 1962.
- [9] Nastasescu C, Oystaeyen FV. Methods of Graded Rings. New York, NY, USA: Springer-Verlag, 2004.
- [10] Nikmehr MJ. Strongly semicommutative rings relative to a monoid. Ukrainian Math J 2014; 66: 1715-1730.
- [11] Passman DS. Infinite Crossed Products. New York, NY, USA: Academic Press, 1989.
- [12] Rege MB, Chhawchharia S. Armendariz rings. Proc Japan Acad Ser A Math Sci 1997; 73: 14-17.
- [13] Yang G, Du RJ. Rings over which polynomial rings are semicommutative. Vietnam J Math 2009; 37: 527-535.
- [14] Zhao L, Zhou YQ. Generalized Armendariz properties of crossed product type. Glasgow Math J 2016; 58: 313-323.