Combinatorial Matrix Theory

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Semirings And Affine Equations Over Them Theory And Applications

Idempotents yield much insight in the structure of finite semigroups and semirings. In this article, we obtain some results on (multiplicatively) idempotents of the endomorphism semiring of a finite chain. We prove that the set of all idempotents with certain fixed points is a semiring and find its order. We further show that this semiring is an ideal in a well known semiring. The construction of an equivalence relation such that any equivalence class contain just one idempotent is proposed. In our main result we prove that such equivalence class is a semiring and find his order. We prove that the set of all idempotents with certain jump points is a semiring.

Idempotent elements of the endomorphism semiring of a finite chain

This paper presents a brief survey of the current state of the derivations in semirings.This paper presents a brief survey of the current state of the derivations in semirings.

Derivations on semirings

In this paper, the author gives a description of the derivatives in UTMn(S), the semiring of upper triangular matrices over an additively idempotent semiring S. The main result states that an arbit...

Derivations of upper triangular matrix semirings

Idempotents yield much insight in the structure of finite semigroups and semirings. In this article, we obtain some results on (multiplicatively) idempotents of the endomorphism
semiring of a finite chain. We prove that the set of all idempotents with certain fixed points is a semiring and find its order. We further show that this semiring is an ideal in a well-known semiring. The construction of an equivalence relation such that any equivalence class contains just one idempotent is proposed. In our main result we prove that such an equivalence class is a semiring and find its order. We prove that the set of all idempotents with certain jump points is a semiring.

https://downloads.hindawi.com/archive/2013/120231.pdf

Idempotent Elements of the Endomorphism Semiring of a Finite Chain

In this article we construct examples of derivations in matrix semirings. We study hereditary and inner derivations, derivatives of diagonal, triangular, Toeplitz, circulant matrices and of matrices of other forms and prove theorems for derivatives of matrices of these forms.

Derivatives of triangular, Toeplitz, circulant matrices and matrices of other forms over semirings

The aim of this paper is the investigation of the derivations in an endomorphism semiring of a finite chain. Such semiring can be represented as a simplex and its subsimplices are left ideals of th...

Projections on right and left ideals of endomorphism semiring which are derivations

The aim of this paper is the investigation of derivations in semiring of polynomials over idempotent semiring. For semiring S[x], where S is a commutative idempotent semiring we construct derivatio...

Dimitrinka Vladeva

Papers

Idempotent elements of the endomorphism semiring of a finite chain

Idempotent Elements of the Endomorphism Semiring of a Finite Chain

Derivatives of triangular, Toeplitz, circulant matrices and matrices of other forms over semirings

Projections on right and left ideals of endomorphism semiring which are derivations

Derivations of polynomial semirings