PARTIAL ORDER IN MODULE OVER A MATRIX NEARRING

Authors

S. Tapatee, Manipal Institute of Technology
B. S. Kedukodi, Manipal Institute of Technology
P. Pallavi, Manipal Institute of Technology
P. K. Harikrishnan, Manipal Institute of Technology

Document Type

Article

Publication Title

International Journal of Applied Mathematics

Abstract

Let Mn (N) be a matrix nearring over the nearring N with identity and let Nⁿ be the direct sum of n-copies of the group (N, +). We introduce a partial order in the Mn (N)-group Nⁿ corresponding to the partial order in N-group (over itself). We define a positive cone in Mn (N)-group Nⁿ and obtain its characterization. For a convex ideal ofN N, the corresponding ideal in Mn (N)-group Nⁿ is described; and conversely, if I is a convex ideal in Mn (N)-group Nⁿ, then the ideal I∗∗ is convex in N (over itself). This establishes the one-one correspondence between the convex ideals of the p.o. N-groupN N and those of p.o. Mn (N)-group Nⁿ.

First Page

391

Last Page

401

DOI

10.12732/ijam.v38i3.6

Publication Date

1-1-2025

Recommended Citation

Tapatee, S.; Kedukodi, B. S.; Pallavi, P.; and Harikrishnan, P. K., "PARTIAL ORDER IN MODULE OVER A MATRIX NEARRING" (2025). Open Access archive. 14026.
https://impressions.manipal.edu/open-access-archive/14026