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On some distinguished classes of elements of multiplicative lattices
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On some distinguished classes of elements of multiplicative lattices

Sfundo Cebolenkosi Gumede
Master of Science (MSc), University of Johannesburg
2025
Handle:
https://hdl.handle.net/10210/520041

Abstract

This dissertation investigates certain distinguished classes of elements of multiplicative lattices, focussing on their algebraic properties, structural characteristics and their relationships with other elements of the multiplicative lattice. We provide detailed characterisations of these distinguished elements in multiplicative lattices. Additionally we provide abstract versions of some ring theoretic results in commutative rings to multiplicative lattices, focusing on those that have not been studied more frequently. The results discussed in this dissertation may provide new insights into structural theory of multiplicative lattices. This work lays foundation for future investigations into more complex lattice structures and their potential applications in other branches of mathematics.
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