A module over a ring is a generalization of the notion of vector space over a field, wherein the corresponding scalars are the elements of an arbitrary given ring and a multiplication is defined between elements of the ring and elements of the module.

- Pakistan Mathematical SocietyThe PakMS was registered on 16th November 2001. The Society had to apply again for registration under the ACT XXI of 1860 to meet the requirement of the Pakistan Science Foundation for registration of the society with it. It was finally registered under this Act on 17th February 2003.
- American Mathematical SocietyThe American Mathematical Society has a bicameral governance structure consisting of the Council (created when the Society’s constitution was ratified in December 1889) and the Board of Trustees (created when the Society was incorporated in May 1923).
- London Mathematical SocietyThe London Mathematical Society is the major UK learned society for mathematics. The Society's activities include publishing journals and books, providing grants to support mathematics and organising scientific meetings and lectures.

- European Mathematical SocietyThe European Mathematical Society is a learned society representing mathematicians throughout Europe. It promotes the development of all aspects of mathematics in Europe, in particular
- Canadian Mathematical SocietiesThe Canadian Mathematical Society (CMS) was originally conceived in June 1945 as the Canadian Mathematical Congress. The founding members hoped that "this congress [would] be the beginning of important mathematical development in Canada".
- Mathematical Programming Societyinternational organization dedicated to the promotion and the maintenance of high professional standards in the subject of mathematical programming. It is incorporated as a non-profit tax-exempt scientific organization in the United States.
- Foundation of Computational MathematicsFoundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics,