ISSN : 2488-8648
International Journal of Basic Science and Technology
A publication of the Faculty of Science, Federal University Otuoke, Bayelsa State
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ISSN : 2488-8648
Home About IJBST For Authors Issues Useful Downloads Contact
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×published date:2022-Apr-29
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Abstract
A monoid M = (M, . , e) is an algebraic structure which under a defined binary operation possesses the property of associativity and has identity element. i.e. for all x,y,z in M, the operation x.(y.z) = (x.y).z and x.e = e.x = e in the operation (x,y) →(x.y). If M is a monoid and R in M an equivalence relation on M satisfying the property xRu and yRv implies x.y R u.v , then R is a congruence relation. The usefulness of function to monoids transformation in connection to word construction in computer arithmetic is investigated. Machine approaches derived from homomorphic theory are used to demonstrate the linked concepts of simulation and realisation. Some theorems about algebraic structures and machines are given and demonstrated with appropriate illustrations.
Keywords: Monoid, Algebraic Structure, Binary Operation, Computer Arithmetic, Homomorphic Theory
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