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
SN - 1018-6301
VL - 48
SP - 3195
EP - 3209
JO - Bulletin of the Iranian Mathematical Society
JF - Bulletin of the Iranian Mathematical Society
IS - 6
ER -