Maximal Subgroups of the Multiplicative Semigroup of $2\times 2$ Supertropical Matrices

, Meenakshi; Devi, Pooja

Indian Journal of Mathematics

Maximal Subgroups of the Multiplicative Semigroup of $2\times 2$ Supertropical Matrices

Author(s): Meenakshi Meenakshi Srinivasa Ramanujan Department of Mathematics,
Central University of Himachal Pradesh,
Shahpur, Kangra, 176206, Himachal Pradesh,
India. meenakshicuhp@hpcu.ac.in; meenakshithakur490@gmail.com , Pooja Devi Pooja Devi Srinivasa Ramanujan Department of Mathematics,
Central University of Himachal Pradesh,
Shahpur, Kangra, 176206, Himachal Pradesh,
India. poojakhanna910@gmail.com

Vol. 67, No. 2 (2025) • pp. 221–252

Published 09-07-2026 Article History Received 10-01-2026 Revised 02-05-2026 Published 09-07-2026

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Abstract

We give a complete characterisation of Green’s relations $\mathscr{L},\mathscr{R},\mathscr{H}$, $\mathscr{D}$ and $\mathscr{J}$ in the multiplicative semigroup of $2\times 2$ supertropical matrices. We determine the maximal subgroups of the semigroup $M_2(\mathbb{T})$ by finding the $\mathscr{R}- classes$ containing idempotents, followed by the identification of $\mathscr{H}- classes$.

Keywords

Supertropical algebra, Semigroup, Maximal subgroup.

2020 Mathematics Subject Classification

12K10, 06F05, 20E28.

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Allahabad Mathematical Society

Maximal Subgroups of the Multiplicative Semigroup of $2\times 2$ Supertropical Matrices

Abstract

Keywords

2020 Mathematics Subject Classification

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