TY - JOUR

T1 - Partial Order in Matrix Nearrings

AU - Sahoo, Tapatee

AU - Meyer, Johannes Hendrik

AU - Panackal, Harikrishnan

AU - Srinivas, Kedukodi Babushri

AU - Prasad, Kuncham Syam

N1 - Funding Information:
The authors express their deep gratitude to the referee(s)/editor(s) for their careful reading of the manuscript, and valuable suggestions that have definitely improved the paper. S. Tapatee, P.K. Harikrishnan, B.S. Kedukodi, S.P. Kuncham acknowledge Manipal Institute of Technology (MIT), Manipal Academy of Higher Education, Manipal, India for their kind encouragement. J. H. Meyer acknowledges the University of the Free State, Bloemfontein, South Africa.
Publisher Copyright:
© 2022, The Author(s).

PY - 2022/12

Y1 - 2022/12

N2 - Let N be a zero-symmetric (right) nearring with identity. We introduce a partial order in the matrix nearring corresponding to the partial order (defined by Pilz in Near-rings: the theory and its applications, North Holland, Amsterdam, 1983) in N. A positive cone in a matrix nearring is defined and a characterization theorem is obtained. For a convex ideal I in N, we prove that the corresponding ideal I∗ is convex in Mn(N) , and conversely, if I is convex in Mn(N) , then I∗ is convex in N. Consequently, we establish an order-preserving isomorphism between the p.o. quotient matrix nearrings Mn(N) / I∗ and Mn(N′)/(I′)∗ where I and I′ are the convex ideals of p.o. nearrings N and N′, respectively. Finally, we prove some properties of Archimedean ordering in matrix nearrings corresponding to those in nearrings.

AB - Let N be a zero-symmetric (right) nearring with identity. We introduce a partial order in the matrix nearring corresponding to the partial order (defined by Pilz in Near-rings: the theory and its applications, North Holland, Amsterdam, 1983) in N. A positive cone in a matrix nearring is defined and a characterization theorem is obtained. For a convex ideal I in N, we prove that the corresponding ideal I∗ is convex in Mn(N) , and conversely, if I is convex in Mn(N) , then I∗ is convex in N. Consequently, we establish an order-preserving isomorphism between the p.o. quotient matrix nearrings Mn(N) / I∗ and Mn(N′)/(I′)∗ where I and I′ are the convex ideals of p.o. nearrings N and N′, respectively. Finally, we prove some properties of Archimedean ordering in matrix nearrings corresponding to those in nearrings.

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U2 - 10.1007/s41980-022-00689-w

DO - 10.1007/s41980-022-00689-w

M3 - Article

AN - SCOPUS:85125468331

VL - 48

SP - 3195

EP - 3209

JO - Bulletin of the Iranian Mathematical Society

JF - Bulletin of the Iranian Mathematical Society

SN - 1018-6301

IS - 6

ER -