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pro vyhledávání: '"Kepka, Tomáš"'
Autor:
Kepka, Tomáš, Korbelář, Miroslav
Let $S$ be an additively idempotent semiring and $\mathbf{M}_n(S)$ be the semiring of all $n\times n$ matrices over $S$. We characterize the conditions of when the semiring $\mathbf{M}_n(S)$ is congruence-simple provided that the semiring $S$ is eith
Externí odkaz:
http://arxiv.org/abs/2305.00587
Publikováno v:
Internat. J. Algebra Comput. 34 (2024), 407-424
It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a semiring $S$,
Externí odkaz:
http://arxiv.org/abs/2303.06921
Let $S$ be a multiplicatively idempotent congruence-simple semiring. We show that $|S|=2$ if $S$ has a multiplicatively absorbing element. We also prove that if $S$ is finite then either $|S|=2$ or $S\cong End(L)$ or $S^{op}\cong End(L)$ where $L$ is
Externí odkaz:
http://arxiv.org/abs/2207.08160
We provide a classification of congruence-simple semirings with a multiplicatively absorbing element and without non-trivial nilpotent elements.
Externí odkaz:
http://arxiv.org/abs/2207.05448
Akademický článek
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Autor:
Kepka, Tomáš, Korbelář, Miroslav
Publikováno v:
Journal of Algebra & Its Applications; Jan2025, Vol. 24 Issue 1, p1-20, 20p
Autor:
Kepka, Tomáš, Korbelář, Miroslav
Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively divisible semiri
Externí odkaz:
http://arxiv.org/abs/1401.2836
Autor:
Kepka, Tomáš, Korbelář, Miroslav
A polynomial $p\in\mathbb{R}[x]$ is a divisor of some polynomial $0\neq f\in\mathbb{R}[x]$ with non-negative coefficients if and only if $p$ does not have a positive real root. The lowest possible degree of such $f$ for a given $p$ is known for quadr
Externí odkaz:
http://arxiv.org/abs/1210.6868
Publikováno v:
Comment. Math. Univ. Carolin. 51 (2010), no. 2, 267-277
In math.GR/0510298, we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show t
Externí odkaz:
http://arxiv.org/abs/math/0601077
Publikováno v:
Comment. Math. Univ. Carolin. 49 (2008), no. 2, 249-257
In math.GR/0510298, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the equational class of (pointed) F-quasigroups and the equation
Externí odkaz:
http://arxiv.org/abs/math/0512244