Clones of Finite Idempotent Algebras with Strictly Simple Subalgebras [electronic resource]
We determine the clone of a finite idempotent algebra A that is not simple and has a unique nontrivial subalgebra S with more than two elements. Under these conditions, the proper subalgebras and the quotient algebra of A are finite idempotent strictly simple algebras of size at least 3 and...
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| Format: | Thesis Electronic eBook |
| Language: | English |
| Published: |
2011.
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| Summary: | We determine the clone of a finite idempotent algebra A that is not simple and has a unique nontrivial subalgebra S with more than two elements. Under these conditions, the proper subalgebras and the quotient algebra of A are finite idempotent strictly simple algebras of size at least 3 and it is known that such algebras are either affine, quasiprimal, or of a third classification. We focus on the first two cases. By excluding binary edge blockers from the relational clone when S is affine and by excluding ternary edge blockers from the relational clone together with an additional condition on the subuniverses of A2 when S is quasiprimal, we give a nice description of the generating set of the relational clone of A . Thus, by the Galois connection between operations and relations, we determine the clone of A. |
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| Item Description: | Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: 4051. Adviser: Agnes Szendrei. |
| Physical Description: | 136 pages. |
| ISBN: | 9781124620541 |