DENUMERABLE PRODUCT SPACES OF PSEUDOQUOTIENTS I

Full Article - PDF

Published: 2019-08-03

Page: 108-122


M. C. OBI *

Department of Mathematics, Federal University of Technology Owerri, Nigeria.

H. C. AZUBUIKE

Department of Mathematics, Federal University of Technology Owerri, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

A space of pseudoquotients ß(X,G) is defined as the set of equivalence classes of pairs (x, g), where xX, an arbitrary non-empty set, and gG, a commutative semigroup acting on X such that (x, g)~(y, h) if hx = gy. In this paper, we shall construct the pseudoquotient space ßXi,ΠGi) where X is replaced by a cartesian product of countably infinite non-empty sets Xi and G by a direct product denumerable commutative semigroups Gi, i ∈ I an indexing set, such that ΠGi acts injectively on ΠXi.

Keywords: Pseudoquotients, equivalence, semigroup, spaces.


How to Cite

OBI, M. C., & AZUBUIKE, H. C. (2019). DENUMERABLE PRODUCT SPACES OF PSEUDOQUOTIENTS I. Asian Journal of Mathematics and Computer Research, 26(2), 108–122. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/4648

Downloads

Download data is not yet available.