На 2 декември 2022 г. (петък) от 13:00 ч. ще се проведе дистанционно заседание на семинара по „Алгебра и логика”.

Доклад на тема:

## Derivations of upper triangular matrix semirings

ще изнесе Димитринка Владева.

Абстракт. The motivation for this talk is the problem how to represent a derivation of a matrix ring and of an additively idempotent matrix semiring as a sum of well-known derivations.

The results of two of my articles, published in 2022, will be compared and we will draw conclusions about the advantages and disadvantages of these results.
We begin by considering the nature of derivations of triangular matrices over an additively idempotent semiring R generated by left and right semicentral idempotents. Then we construct a semiring D of these derivations and find a basis of D, considered as an R-semimodule. The main result of the first article states that an arbitrary derivation of UTMn(R) (the semiring of upper triangular matrices over an additively idempotent semiring R) is a linear combination of a derivations from the basis of R-semimodule D. When R is an associative ring with identity and UTMn(R) is the ring of upper triangular n x n matrices over R we propose a basis of an additive group D of derivations of UTM_n(R) consisting of derivations δ_i such that δ_i(A) = [e_ii,A], where A ∈UTM_n(R) and e_ii are diagonal matrix units for i = 2, …, n. The main result states that if D is an arbitrary derivation of the ring UTM_n(R) and A ∈UTM_n(R), then there are matrices, such that the derivative D(A) is a linear combination of the values of derivations δ_i ∈D, i = 2, …, n, of these matrices with coefficients the entries of the matrix A.

Семинарът ще се проведе посредством платформата Zoom и всеки желаещ може да се присъедини като последва линка:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Dec 02, 2022 01:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647

От секция „Алгебра и логика” на ИМИ – БАН
http://www.math.bas.bg/algebra/seminarAiL/
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