Pseudo d-algebras |
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Authors: | Young Bae Jun J Neggers |
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Affiliation: | a Department of Mathematics Education, Gyeongsang National University, Chinju 660 701, Republic of Korea b Department of Mathematics, Hanyang University, Seoul 133 791, Republic of Korea c Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487 0350, USA |
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Abstract: | We introduce the notion of a pseudo d-algebra as a generalization of the idea of a d-algebra. The class of pseudo d-algebras can be included in the class of coupled d-algebras. We show that the class of pseudo d-algebras behaves well with respect to standard mappings such as direct products and standard mappings such as homomorphisms. Indeed, we are able to prove a fundamental theorem of homomorphisms and we are able to identify kernel objects as d-ideals in this theory. We also discuss several large classes of examples of pseudo d-algebras which occur in different settings and we identify properties sufficient for or equivalent to membership in important subclasses of the class of pseudo d-algebras in these settings. |
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Keywords: | 06F35 |
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