JP Journal of Algebra, Number Theory and Applications
Volume 47, Issue 2, Pages 181 - 215
(August 2020) http://dx.doi.org/10.17654/NT047020181 |
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SYSTEMS OF ω-LINEAR BALANCES OVER SYMMETRIZED OMEGA ALGEBRA
Mesfer Alqahtani, Cenap Özel, Hanifa Zekraoui and Ibtesam Alshammari
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Abstract: In this paper, we study the existence and uniqueness of signed solutions for systems of ω-linear balances over the symmetrized omega algebra. Furthermore, we generalize the main algebraic features of balances and define the rank, linear combination, linear dependence and linear independence over the symmetrized omega algebra. Definitions and some related properties of the determinant and adjoint matrix over the symmetrized omega algebra are introduced. |
Keywords and phrases: tropical geometry, idempotent semirings, omega algebra, symmetrized omega algebra, ω-linear dependence, ω-linear independence, ω-linear balances, matrix.
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