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3 Discussiones Mathematicae - General Algebra and Applications

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Equational bases for weak monounary varieties

100%

Bińczak G.

Discussiones Mathematicae - General Algebra and Applications

2002

tom 22

nr 1

87-100

It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.

Some finite directly indecomposable non-monogenic entropic quasigroups with quasi-identity

63%

Bińczak G. , Kaleta J.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 1

5-26

In this paper we show that there exists an infinite family of pairwise non-isomorphic entropic quasigroups with quasi-identity which are directly indecomposable and they are two-generated.

The table of characters of some quasigroups

63%

Bińczak G. , Kaleta J.

Discussiones Mathematicae - General Algebra and Applications

2007

tom 27

nr 2

147-167

It is known that (ℤₙ,-ₙ) are examples of entropic quasigroups which are not groups. In this paper we describe the table of characters for quasigroups (ℤₙ,-ₙ).