<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic systems whose objects possessing the hyperoperations or multi-valued operation. We introduce categories in which for objects <italic>A</italic> and <italic>B</italic>, the class of all morphisms from <italic>A</italic> to <italic>B</italic> denoted by <italic>Mor</italic>(<italic>A, B</italic>), admits an algebraic hyperstructures, such as semihypergroup or hypergroup. In this regards we introduce the various types of pre-semihyperadditive categories. Also, we construct some (pre-)semihyperadditive categories by introducing a class of hypermodules named general Krasner hypermodules. Finally, we investigate some properties of these categories.</p></abstract>

In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic systems whose objects possessing the hyperoperations or multi-valued operation. We introduce categories in which for objects A and B, the class of all morphisms from A to B denoted by Mor(A, B), admits an algebraic hyperstructures, such as semihypergroup or hypergroup. In this regards we introduce the various types of pre-semihyperadditive categories. Also, we construct some (pre-)semihyperadditive categories by introducing a class of hypermodules named general Krasner hypermodules. Finally, we investigate some properties of these categories.

Pre-semihyperadditive Categories

School of Mathematics, Statistics and Computer Science, Collage of Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Pre-semihyperadditive Categories"}

In this paper we extend the notion of classical (pre-)semiadditive category to (pre-)semihyperadditive category. Algebraic hyperstructures are algebraic...

Pre-semihyperadditive Categories

Published Online: Mar 02, 2019

Page range: 269 - 288

Received: Jul 25, 2017

Accepted: Jan 27, 2018

DOI: https://doi.org/10.2478/auom-2019-0014

Keywords
Pre-semihyperadditive Category, Pre-hyperadditive Category, Pre-canonical Hyperadditive Category, Hypercategory

© 2019 H. Shojaei et al., published by Sciendo

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

Pre-semihyperadditive Categories

Published Online: Mar 02, 2019

Page range: 269 - 288

Received: Jul 25, 2017

Accepted: Jan 27, 2018

DOI: https://doi.org/10.2478/auom-2019-0014

KeywordsPre-semihyperadditive Category, Pre-hyperadditive Category, Pre-canonical Hyperadditive Category, Hypercategory

© 2019 H. Shojaei et al., published by Sciendo

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

Keywords
Pre-semihyperadditive Category, Pre-hyperadditive Category, Pre-canonical Hyperadditive Category, Hypercategory