1. bookVolume 30 (2022): Issue 1 (February 2022)
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
access type Open Access

Divisible hypermodules

Published Online: 12 Mar 2022
Volume & Issue: Volume 30 (2022) - Issue 1 (February 2022)
Page range: 57 - 74
Received: 07 May 2021
Accepted: 19 Jul 2021
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
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.

Keywords

MSC 2010

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