Generalized derived algebras and generalized induced algebras
Substituting for the fundamental operations of an algebra term operations we get a new algebra of the same type, called a generalized derived algebra. Such substitutions are called generalized hypersubstitutions. Generalized hypersubstitutions can also be applied to every equation of a fully invaria...
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| Main Authors: | , |
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| Format: | Article |
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World Scientific Publishing Co. Pte Ltd
2015
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| Subjects: | |
| Online Access: | http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=79961244144&origin=inward http://cmuir.cmu.ac.th/handle/6653943832/38600 |
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| Institution: | Chiang Mai University |
| Summary: | Substituting for the fundamental operations of an algebra term operations we get a new algebra of the same type, called a generalized derived algebra. Such substitutions are called generalized hypersubstitutions. Generalized hypersubstitutions can also be applied to every equation of a fully invariant equational theory. The equational theory generated by the resulting set of the equations induces on every algebra of the type under consideration a fully invariant congruence relation. If we factorize the generalized derived algebra by this fully invariant congruence relation we will obtain an algebra which we call generalized induced algebra. In this paper, we prove some properties which transfer the starting algebras to generalized derived algebras and to generalized induced algebras. © 2010 World Scientific Publishing Company. |
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