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ЖУРНАЛЫ // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Архив

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, номер 2, страницы 3–16 (Mi basm473)

Research articles

Quotient structure and chain conditions on quasi modules

Sandip Jana, Supriyo Mazumder

Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India

Аннотация: Quasi module is an axiomatisation of the hyperspace structure based on a module. We initiated this structure in our paper [2]. It is a generalisation of the module structure in the sense that every module can be embedded into a quasi module and every quasi module contains a module. The structure of quasi module is a conglomeration of a commutative semigroup with an external ring multiplication and a compatible partial order. In the entire structure partial order has an intrinsic effect and plays a key role in any development of the theory of quasi modules. In the present paper we have discussed the quotient structure of a quasi module by introducing a congruence suitably. Also we introduce the concept of chain conditions on quasi modules and prove some theorems related to chain conditions.

Ключевые слова и фразы: module, quasi module, Noetherian quasi module, Artinian quasi module.

MSC: 08A99, 13C99, 06F99

Поступила в редакцию: 03.01.2017

Язык публикации: английский



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