Characterization of Chain as a Regular Semi Group
R. Kehinde and S.O. Makanjuola
DOI : 10.3844/jmssp.2008.199.200
Journal of Mathematics and Statistics
Volume 4, Issue 4
Problem Statement: There are some special classes of semi group namely: regular and eventually regular, abundant, orthodox, quasi-adequate. The objective of this study were to: (i) Define a new class of semi group on a Poset and give related examples (ii) Study and establish conditions that characterized Chain as a regular semi group. Approach: Tests of some of characteristics of semi group like associativity, commutativity, and regular semi group were carried out on this new class. Results: Conditions were obtained that showed it is associative and regular. Conclusion: Hence the results suggest that since Chain is regular, there are many other things we can still do this with class of semi group such as: (i) Whether one can characterize all the Green's equivalences and their starred analogues (ii) Whether one can characterize all the congruencies of the given semi group (iii) Whether one characterize all the subsemigroups of the given semi group.
© 2008 R. Kehinde and S.O. Makanjuola. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.