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On sets related to maximal clones

100%

Susanti Y., Denecke K.

Discussiones Mathematicae - General Algebra and Applications

2012

tom 32

nr 1

101-114

For an arbitrary h-ary relation ρ we are interested to express n-clone Polⁿρ in terms of some subsets of the set of all n-ary operations Oⁿ(A) on a finite set A, which are in general not clones but we can obtain Polⁿρ from these sets by using intersection and union. Therefore we specify the concept a function preserves a relation and moreover, we study the properties of this new concept and the connection between these sets and Polⁿρ. Particularly we study $R_{a̲,b}^{n,k}$ for arbitrary partial order relations, equivalence relations and central relations.

Four-part semigroups - semigroups of Boolean operations

81%

Jampachon P., Susanti Y., Denecke K.

Discussiones Mathematicae - General Algebra and Applications

2012

tom 32

nr 1

115-136

Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

2 Denecke K.

2 Susanti Y.

1 Jampachon P.

2 2012

Wyniki wyszukiwania

On sets related to maximal clones

Four-part semigroups - semigroups of Boolean operations