<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal injective hypermodules. First we define the concept of zero-divisors over a hypermodule and based on it we introduce a new class of hypermodules, the one of divisible hypermodules. After presenting some of their fundamental properties, we will show that the class of normal injective <italic>R</italic>-hypermodules <italic>M</italic> and the class of divisible <italic>R</italic>-hypermodules <italic>M</italic> coincide whenever <italic>R</italic> is a hyperring with no zero-divisors over <italic>M</italic>. Finally, we answer to an open problem related to canonical hypergroups. In particular, we show that any canonical hypergroup can be endoweded with a ℤ-hypermodule structure and it is a normal injective ℤ-hypermodule if and only if it is a divisible ℤ-hypermodule.</p>
</abstract>

The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal injective hypermodules. First we define the concept of zero-divisors over a hypermodule and based on it we introduce a new class of hypermodules, the one of divisible hypermodules. After presenting some of their fundamental properties, we will show that the class of normal injective R-hypermodules M and the class of divisible R-hypermodules M coincide whenever R is a hyperring with no zero-divisors over M. Finally, we answer to an open problem related to canonical hypergroups. In particular, we show that any canonical hypergroup can be endoweded with a ℤ-hypermodule structure and it is a normal injective ℤ-hypermodule if and only if it is a divisible ℤ-hypermodule.

Divisible hypermodules

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Divisible hypermodules"}

The article is motivated by the recently published studies on injective and projective hypermodules. We present here a new characterization of the normal...

Divisible hypermodules

Published Online: Mar 12, 2022

Page range: 57 - 74

Received: May 07, 2021

Accepted: Jul 19, 2021

DOI: https://doi.org/10.2478/auom-2022-0004

Keywords
Normal injective hypermodule, Zero-divisor, Divisible hypermodule, Canonical hypergroup

© 2022 Hashem Bordbar et al., published by Sciendo

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

Divisible hypermodules

Published Online: Mar 12, 2022

Page range: 57 - 74

Received: May 07, 2021

Accepted: Jul 19, 2021

DOI: https://doi.org/10.2478/auom-2022-0004

KeywordsNormal injective hypermodule, Zero-divisor, Divisible hypermodule, Canonical hypergroup

© 2022 Hashem Bordbar et al., published by Sciendo

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

Keywords
Normal injective hypermodule, Zero-divisor, Divisible hypermodule, Canonical hypergroup