Dietrich Burde,Karel Dekimpe,Mina Monadjem
Dietrich Burde
We study the existence of post-Lie algebra structures on pairs of Lie algebras ( g , n ) , where one of the algebras is perfect non-semisimple, and the other one is abelian, nilpotent non-abelian, solvable non-nilpotent, simple, semisimple...
Aqsa Bashir,Alfred Geroldinger,Andreas Reinhart
Aqsa Bashir
A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is know...
Lukas Andritsch
Lukas Andritsch
We consider GL m -dimers of triangulations of regular convex n-gons, which give rise to a dimer model with boundary Q and a dimer algebra Λ Q . Let eb be the sum of the idempotents of all the boundary vertices, and B Q : = e b Λ Q e...
Chimere Stanley Anabanti,Sarah Beatrice Hart,Michael C Slattery
Chimere Stanley Anabanti
Mazurov asked whether a group of exponent dividing 12, which is generated by x, y and z subject to the relations x 3 = y 2 = z 2 = ( x y ) 3 = ( y z ) 3 = 1 , has order at most 12. We show that if such a group is finite, then the answ...
Alfred Geroldinger,Moshe Roitman
Alfred Geroldinger
A commutative integral domain is primary if and only if it is one-dimensional and local. A domain is strongly primary if and only if it is local and each nonzero principal ideal contains a power of the maximal ideal. Hence, one-dimensional ...
A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator [0.03%]
具有无平方因数分母的整值多项式绝对不可约的一个图论判定准则
Sophie Frisch,Sarah Nakato
Sophie Frisch
An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of the ring Int ( D ) = { f ∈ K [ x ] | f ( D ) ⊆ D ...
Bruce Olberding,Andreas Reinhart
Bruce Olberding
In this article, we investigate the concept of radical factorization with respect to finitary ideal systems of cancellative monoids. We present new characterizations for r-almost Dedekind r-SP-monoids and provide specific descriptions of t-...
Classification of Rota-Baxter operators on semigroup algebras of order two and three [0.03%]
二次和三次半群代数上的Rota-Baxter算子的分类
Shanghua Zheng,Li Guo,Markus Rosenkranz
Shanghua Zheng
In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defin...
Triviality of differential Galois cohomology of linear differential algebraic groups [0.03%]
线性差分代数群的微分Galois上同调的平凡性问题
Andrei Minchenko,Alexey Ovchinnikov
Andrei Minchenko
For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard-Vessiot, and linearly differentia...
Rota-Baxter operators and post-Lie algebra structures on semisimple Lie algebras [0.03%]
半单李代数上的Rota-Baxter算子和后Lie代数结构
Dietrich Burde,Vsevolod Gubarev
Dietrich Burde
Rota-Baxter operators R of weight 1 on n are in bijective correspondence to post-Lie algebra structures on pairs ( g , n ) , where n is complete. We use such Rota-Baxter operators to study the existence and classification of post-Lie algeb...