The Morphic property in modules and near-rings

dc.contributor.author Kimuli, Philly Ivan
dc.date.accessioned 2022-08-24T14:16:35Z
dc.date.available 2022-08-24T14:16:35Z
dc.date.issued 2022-08-22
dc.description A dissertation submitted to the Directorate of Research and Graduate Training in partial fulfillment of the requirements for the award of the Degree of Doctor of Philosophy in Mathematics of Makerere University en_US
dc.description.abstract We introduce and study weakly-morphic modules and their properties. In particular, we show that a finitely generated $\Bbb Z$-module is weakly-morphic if and only if it is finite. Hence a finitely generated Abelian group is morphic if and only if it is weakly-morphic as a $\Bbb Z$-module and each of its primary components is of the form $(\Bbb Z/p^k\Bbb Z)^n$ for some non-negative integers $n$ and $k$. Using these weakly-morphic modules, different notions of a regular module are characterised. We show that, under some special conditions, weakly-morphic property on reduced (respectively, co-reduced) (cyclic) sub-modules reveals the kind of regularity a module will have. Lastly, we study left-morphic near-ring elements and show that the class of left-morphic regular near-rings is properly contained between the classes of left strongly regular and unit-regular near-rings. en_US
dc.description.sponsorship Makerere-Sida Bilateral Research Program en_US
dc.identifier.citation Kimuli, P. I. (2022). The Morphic property in modules and near-rings. (MakIR) (Unpublished PhD thesis). Makerere University , Kampala,Uganda. en_US
dc.identifier.uri http://hdl.handle.net/10570/10763
dc.language.iso en en_US
dc.subject Regular Module en_US
dc.subject Reduced module en_US
dc.subject (weakly-)morphic module en_US
dc.subject left-morphic near-ring en_US
dc.title The Morphic property in modules and near-rings en_US
dc.type Thesis en_US
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