Jordan derivations on semirings of triangular matrices
Dimitrinka Vladeva
TL;DR
This paper investigates Jordan derivations on triangular matrices over additively idempotent semirings, establishing conditions under which derivatives can be constructed by zeroing dense submatrices.
Contribution
It characterizes the set of Jordan derivations for triangular matrices over additively idempotent semirings, introducing a method to derive matrices by zeroing dense submatrices.
Findings
Derivations can be obtained by zeroing dense submatrices.
The set of such derivations is explicitly characterized.
The results extend understanding of Jordan derivations in semiring contexts.
Abstract
We explore Jordan derivations of triangular matrices with entries from an additively idempotent semiring. The main result states that for any matrix A over additively idempotent semiring, if we put all the elements of the family of dense submatrices of A to be zeroes, we find a derivative of A. The set of derivations of this type is established.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Polynomial and algebraic computation