Extensions of semicommutative rings
Date
2011
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Abstract
We introduce two generalizations of semicommutative rings, i. e. quasi-semicommutative rings and context SC modules. Various properties of quasi-semicommutative rings are discussed, especially some of the stronger commutativity condit ions (NI, 2-primal, etc.). We also discuss those different classes of rings within some particular class of rings (von Neumann regular, p .p ., semiprime, etc.). Particular emphasis is given to the similarities and differences between quasi-SC and SC rings. Two different generalizations of semicommutativity to modules are also investigated. The first one is context SC modules. Two particular contexts are studied, and the structure of some of the context SC modules is obtained. The other one is a study of t he known class of semicommutative modules. Rings over which all modules are SC are characterized, and we show that some theorems in Chapter 2 can be generalized to modules.
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Bibliography: p. 65-68.
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Citation
Chen, X. (2011). Extensions of semicommutative rings (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4469