Geodesic
Quotient structure and chain conditions on quasi modules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2018), pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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Sandip Jana; Supriyo Mazumder. Quotient structure and chain conditions on quasi modules. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2018), pp. 3-16. http://geodesic.mathdoc.fr/item/BASM_2018_2_a0/

[1] Blyth T. S., Module theory: an approach to linear algebra, Oxford University Press, USA, 1977 | MR | Zbl

[2] Jana S., Mazumder S., “An associated structure of a Module”, Revista de la Academia Canaria de Ciencias, 25 (2013), 9–22 | MR

[3] Mazumder S., Jana S., “Exact Sequence on Quasi Module”, Southeast Asian Bulletin of Mathematics, 41 (2017), 525–533 | MR | Zbl