Kyungpook Mathematical Journal 2022; 62(1): 57-67
Published online March 31, 2022
Copyright © Kyungpook Mathematical Journal.
Valuations on Ternary Semirings
Sumana Pal*, Jayasri Sircar, Pinki Mondal
Department of Mathematics and Statistics, Aliah University, Kolkata 700160, West Bengal, India
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Department of Mathematics, Lady Brabourne College, Kolkata 700017, West Bengal, India
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Sunity Academy, Cooch Behar, West Bengal 736170, India
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Received: October 6, 2020; Revised: September 1, 2021; Accepted: September 6, 2021
In the present study, we introduce a valuation of ternary semiring on an ordered abelian group. Motivated by the construction of valuation rings, we study some properties of ideals in ternary semiring arising in connection with the valuation map. We also explore ternary valuation semirings for a noncommuative ternary division semiring. We further consider the notion of convexity in a ternary semiring and how it is reflected in the valuation map.
Keywords: Valuation, valuation ring, ternary semiring, ternary division semiring