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On \(\hbox {B}_{po}\)-algebras

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Abstract

In this paper, we introduce and investigate the concept of partially ordered B-algebras (or \(\hbox {B}_{po}\)-algebras) and we provide some related properties. A \(\hbox {B}_{po}\)-algebra is an algebra \((X; *, \preceq , 0)\) such that \((X; *, 0)\) is a B-algebra and \(\preceq \) is a partial order on X such that \(\preceq \) is compatible on X, that is, property (M) holds: (M) \(x \preceq y\) implies \(z *(0 *x) \preceq z *(0 *y)\) and \(x *(0 *z) \preceq y *(0 *z)\) for all \(x, y, z \in X\). We also introduce partially ordered quotient B-algebra via \(\hbox {B}_{po}\)-ideal.

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Acknowledgements

The authors would like to thank the referees for the remarks, comments, and suggestions which were incorporated into this revised version.

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Authors and Affiliations

  1. Department of Mathematics, Silliman University, Dumaguete, Philippines

    Alice Mamhot

  2. Department of Mathematics, Negros Oriental State University, Dumaguete, Philippines

    Joemar Endam

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  1. Alice Mamhot
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  2. Joemar Endam
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Correspondence to Joemar Endam.

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Mamhot, A., Endam, J. On \(\hbox {B}_{po}\)-algebras. Afr. Mat. 30, 1237–1248 (2019). https://doi.org/10.1007/s13370-019-00718-8

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  • DOI: https://doi.org/10.1007/s13370-019-00718-8

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