Geodesic
Quotient structure and chain conditions on quasi modules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2018), pp. 3-16.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{BASM_2018_2_a0,
     author = {Sandip Jana and Supriyo Mazumder},
     title = {Quotient structure and chain conditions on quasi modules},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--16},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2018_2_a0/}
}
TY  - JOUR
AU  - Sandip Jana
AU  - Supriyo Mazumder
TI  - Quotient structure and chain conditions on quasi modules
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2018
SP  - 3
EP  - 16
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2018_2_a0/
LA  - en
ID  - BASM_2018_2_a0
ER  - 
%0 Journal Article
%A Sandip Jana
%A Supriyo Mazumder
%T Quotient structure and chain conditions on quasi modules
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2018
%P 3-16
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2018_2_a0/
%G en
%F BASM_2018_2_a0
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. https://geodesic-test.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