DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

T. Kovář

Tomáš Kovář

University of Hradec Králové, Rokitanského 62, 50003 Hradec Králové

email: tomas_kovar@yahoo.com

0009-0001-2619-7994

Title:

On idempotent elements of dually residuated lattice ordered semigroups

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Source:

Discussiones Mathematicae - General Algebra and Applications 44(2) (2024) 479-483

Received: 2023-10-05 , Revised: 2024-02-05 , Accepted: 2024-02-05 , Available online: 2024-09-12 , https://doi.org/10.7151/dmgaa.1465

Abstract:

We show that idempotent elements of a dually residuated lattice ordered semigroup (a DRl-semigroup) form a Brouwerian algebra. Further we show that for any idempotent elements $x,y$ such that $x\leq y$ the interval $[x;y]$ is also a DRL-semigroup.

Primary keywords:

dually residuated lattice ordered semigroup.

Secondary keywords:

Brouwerian algebra, lattice ordered group

References:

  1. T. Kovář, Two remarks on dually residuated lattice ordered semigroups, Math. Slovaca 49 (1999) 17–18.
  2. J. Rachůnek, A duality between algebras of basic logic and bounded representable DRl-monoids, Math. Bohem. 126 (2001) 561–569.
    https://doi.org/10.21136/MB.2001.134199
  3. K.L.N. Swamy, Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965) 105–114.
    https://doi.org/10.1007/BF01360284
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