This thesis presents a partition of the class of homomorphisms between groupoids of n-tuples in a system g = (G,&,@), where G = { a,b,c,d,e }is a set of five elements such that: 1) a is the &-identity and annihilates all elements under @; 2) b is the @-identity; 3) d absorbs all all elements except e under & and all elements except a and e under @; 4) e absorbs all elements under & and all elements except a under @; 5) & is a binary operation on G and is commutative in G; 6) @ is a binary operation on G and is left-distributive over & in G.Matrices over g were examined for characteristics which would determine different atomic properties of homomorphisms. A matrix operation @ was defined, which allowed the homomorphisms of groupoids of the form, (G(n) , &), to be modeled by a matrix equation. Using the atomic proper ties, a partition of the class of homomorphisms between groupoids was developed, and an example of an element in each of its disjoint subsets was presented. A listing of theorems was also derived.Ball State UniversityMuncie, IN 47306
| Identifer | oai:union.ndltd.org:BSU/oai:cardinalscholar.bsu.edu:handle/181476 |
| Date | 03 June 2011 |
| Creators | Grant, David Joseph |
| Contributors | Petrucco, Oswald |
| Source Sets | Ball State University |
| Detected Language | English |
| Format | [v], 59 leaves : ill. ; 28 cm. |
| Source | Virtual Press |
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