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SM ISO690:2012 JANA, Sandip, MAZUMDER, Supriyo. Quotient Structure and Chain Conditions on Quasi Modules. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2018, nr. 2(87), pp. 3-16. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 2(87) / 2018 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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CZU: 512.553 | ||||||
MSC 2010: 08A99, 13C99, 06F99. | ||||||
Pag. 3-16 | ||||||
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Rezumat | ||||||
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 |
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Cuvinte-cheie module, quasi module, Noetherian quasi module, Artinian quasi module. |
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