<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures. </abstract>

In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.

From lattices to Hv-matrices

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"From lattices to Hv-matrices"}

In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices...

From lattices to Hv-matrices

Published Online: Sep 21, 2017

Page range: 209 - 222

Received: Apr 20, 2015

Accepted: Jun 30, 2015

DOI: https://doi.org/10.1515/auom-2016-0055

Keywords
Distributive lattice, Hv-matrix, Hv-ring, Join space, Partially ordered semigroup.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

From lattices to Hv-matrices

Published Online: Sep 21, 2017

Page range: 209 - 222

Received: Apr 20, 2015

Accepted: Jun 30, 2015

DOI: https://doi.org/10.1515/auom-2016-0055

KeywordsDistributive lattice, Hv-matrix, Hv-ring, Join space, Partially ordered semigroup.

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Distributive lattice, Hv-matrix, Hv-ring, Join space, Partially ordered semigroup.