The Morphic property in modules and near-rings

Date
2022-08-22
Authors
Kimuli, Philly Ivan
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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.
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
Keywords
Regular Module, Reduced module, (weakly-)morphic module, left-morphic near-ring
Citation
Kimuli, P. I. (2022). The Morphic property in modules and near-rings. (MakIR) (Unpublished PhD thesis). Makerere University , Kampala,Uganda.