The spectrum of idempotent varieties of algebras with binary operators based on two variable identities.
N.S. Mendelsohn (1978)
Aequationes mathematicae
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Displaying similar documents to “The spectrum of idempotent varieties of algebras with binary operators based on two variable identities. (Short Communication).”
The spectrum of idempotent varieties of algebras with binary operators based on two variable identities.
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This work is devoted to find and study some possible idempotent operators on a finite chain L. Specially, all idempotent operators on L which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum.
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Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.
On reductive and distributive algebras
Anna B. Romanowska (1999)
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The paper investigates idempotent, reductive, and distributive groupoids, and more generally -algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left -step reductive -algebras, and of right -step reductive -algebras, are independent for any positive integers and . This gives a structural description of algebras in...