On bi-topological BCK-algebras

Mohammed, R. A.; Rasheed, Gh. H.; Khalaf, A. B.

doi:10.22436/jmcs.028.03.08

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2023

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“…For more research on these aspects, see the papers [7][8][9]. For some basic and recent papers related to non-associative BCC-algebras and B-filters in this field, we refer to [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Hopf Quasigroup Galois Extensions and a Morita Equivalence

Guo

Wang

2023

Mathematics

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Section: Introductionmentioning

confidence: 99%

Hopf Quasigroup Galois Extensions and a Morita Equivalence

Guo

Wang

2023

Mathematics

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A Morita-Takeuchi Context and Hopf Coquasigroup Galois Coextensions

Guo

Wang

2023

Symmetry

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For H a Hopf quasigroup and C, a left quasi H-comodule coalgebra, we show that the smash coproduct C⋊H (as a symmetry of smash product) is linked to some quotient coalgebra Q=C/CH*+ by a Morita-Takeuchi context (as a symmetry of Morita context). We use the Morita-Takeuchi setting to prove that for finite dimensional H, equivalent conditions for C/Q to be a Hopf quasigroup Galois coextension (as a symmetry of Galois extension). In particular, we consider a special case of quasigroup graded coalgebras as an application of our theory.

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On bi-topological BCK-algebras

Abstract: In this paper, we present the concept of bi-topological BCK-algebra. Several characterizations and properties of this concept are obtained. Also, the concept of BCK-ideal of a BCK-algebra is defined and some of its properties are found.

Cited by 2 publications

References 5 publications

Hopf Quasigroup Galois Extensions and a Morita Equivalence

Hopf Quasigroup Galois Extensions and a Morita Equivalence

A Morita-Takeuchi Context and Hopf Coquasigroup Galois Coextensions

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