<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green’s relation 𝔻 is a congruence relation on residuated skew lattice and its quotient algebra is a residuated lattice. Deductive system and skew deductive system in residuated skew lattices are defined and relationships between them are given and proved. We define branchwise residuated skew lattice and show that a conormal distributive residuated skew lattice is equivalent with a branchwise residuated skew lattice under a condition.</p></abstract>

In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green’s relation 𝔻 is a congruence relation on residuated skew lattice and its quotient algebra is a residuated lattice. Deductive system and skew deductive system in residuated skew lattices are defined and relationships between them are given and proved. We define branchwise residuated skew lattice and show that a conormal distributive residuated skew lattice is equivalent with a branchwise residuated skew lattice under a condition.

On residuated skew lattices

Department of Pure Mathematics, Faculty of Mathematics and Computer

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On residuated skew lattices"}

In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green’s...

On residuated skew lattices

Published Online: Mar 02, 2019

Page range: 245 - 268

Received: Jan 30, 2018

Accepted: Mar 27, 2018

DOI: https://doi.org/10.2478/auom-2019-0013

Keywords
Skew lattice, residuated lattice, residuated skew lattice, Green’s relation, variety, (skew) deductive system

© 2019 Arsham Borumand Saeid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On residuated skew lattices

Published Online: Mar 02, 2019

Page range: 245 - 268

Received: Jan 30, 2018

Accepted: Mar 27, 2018

DOI: https://doi.org/10.2478/auom-2019-0013

KeywordsSkew lattice, residuated lattice, residuated skew lattice, Green’s relation, variety, (skew) deductive system

© 2019 Arsham Borumand Saeid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Skew lattice, residuated lattice, residuated skew lattice, Green’s relation, variety, (skew) deductive system