p-semisimple modules and type submodules

Autor:	E. Momtahan, A. R. Olfati, A. Mozaffarikhah, S. Safaeeyan
Rok vydání:	2019
Předmět:	Zariski topology Pure mathematics Algebra and Number Theory If and only if Applied Mathematics Multiplication Type (model theory) Mathematics
Zdroj:	Journal of Algebra and Its Applications. 19:2050078
ISSN:	1793-6829 0219-4988
DOI:	10.1142/s0219498820500784
Popis:	In this paper, we introduce the concept of [Formula: see text]-semisimple modules. We prove that a multiplication reduced module is [Formula: see text]-semisimple if and only if it is a Baer module. We show that a large family of abelian groups are [Formula: see text]-semisimple. Furthermore, we give a topological characterizations of type submodules (ideals) of multiplication reduced modules ([Formula: see text]-semisimple rings). Moreover, we observe that there is a one-to-one correspondence between type ideals of some algebraic structures on one hand and regular closed subsets of some related topological spaces on the other hand. This also characterizes the form of closed ideals in [Formula: see text].
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9ba3dccfe62d3c5d211d0cc861b5403a https://doi.org/10.1142/s0219498820500784 Zobrazit plný text záznamu