DENUMERABLE PRODUCT SPACES OF PSEUDOQUOTIENTS I

Main Article Content

M. C. OBI
H. C. AZUBUIKE

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.

Article Details

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 http://www.ikprress.org/index.php/AJOMCOR/article/view/4648
Section
Original Research Article