Supplemented and π-Projective Semimodules

  • Muna M. T. Altaee College of Education for Pure Science, University of Babylon, Babylon, Iraq
  • Asaad M. A. Alhossaini College of Education for Pure Science, University of Babylon, Babylon, Iraq
Keywords: Semimodule, supplemented semimodule, π-projective semimodule, lies above a direct summand, coclosed semimodule

Abstract

In modules there is a relation between supplemented and Ï€-projective semimodules. This relation was introduced, explained and investigated by many authors. This research will firstly introduce a concept of "supplement subsemimodule" analogues to the case in modules: a subsemimodule Y of a semimodule W is said to be supplement of  a subsemimodule X if it is minimal with the property X+Y=W. A subsemimodule Y is called a supplement subsemimodule if it is a supplement of some subsemimodule of W. Then, the concept of supplemented semimodule will be defined as follows: an S-semimodule W is said to be supplemented if every subsemimodule of W is a supplement. We also review other types of supplemented semimodules. Previously, the concept of Ï€-projective semimodule was introduced. The main goal of the present study is to explain the relation between the two concepts, supplemented semimodule and Ï€-projective semimodules, and prove these relations by many results.

Published
2020-06-27
How to Cite
Altaee, M. M. T., & Alhossaini, A. M. A. (2020). Supplemented and π-Projective Semimodules. Iraqi Journal of Science, 61(6), 1479-1487. https://doi.org/10.24996/ijs.2020.61.6.28
Section
Mathematics