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of 399
pro vyhledávání: '"20m25"'
The plactic monoid $\mathbf{P}$ of Lascoux and Sch\"{u}tzenberger (1981) plays an important role in proofs of the Littlewood-Richardson rule for computing multiplicities in the linear representation theory of the symmetric group $\mathfrak{S}_n$ and
Externí odkaz:
http://arxiv.org/abs/2411.17619
Autor:
Panpaliya, Ishan
The ascending chain condition on principal ideals (ACCP) is almost always complementary to atomicity within integral domains: in fact, Cohn initially stated that these two conditions were equivalent. This assertion has been shown to be false, however
Externí odkaz:
http://arxiv.org/abs/2411.16151
Autor:
Guerrieri, Lorenzo
Given an integral domain $D$ with quotient field $\mathcal{Q}(D)$, the reciprocal complement of $D$ is the subring $R(D)$ of $\mathcal{Q}(D)$ whose elements are all the sums $\frac{1}{d_1}+\ldots+\frac{1}{d_n} $ for $d_1, \ldots, d_n$ nonzero element
Externí odkaz:
http://arxiv.org/abs/2411.00616
Autor:
Dermenjian, Aram
We define MC left regular bands and study their adjacency graphs. We prove that for thin MC left regular bands, the adjacency graph is particularly nice and is represented by edge labeled graphs where every simple cycle has an even number of edges. C
Externí odkaz:
http://arxiv.org/abs/2410.13130
Let $M$ be a commutative monoid. An element $d \in M$ is called a maximal common divisor of a nonempty subset $S$ of $M$ if $d$ is a common divisor of $S$ in $M$ and the only common divisors in $M$ of the set $\big\{ \frac{s}d : s \in S \big\}$ are t
Externí odkaz:
http://arxiv.org/abs/2410.09251
Autor:
Basu, Rabeya, Mathew, Maria Ann
The elementary action of symplectic and orthogonal groups on unimodular rows of length $2n$ is transitive for $2n \geq \max(4, d+2)$ in the symplectic case, and $2n \geq \max(6, 2d+4)$ in the orthogonal case, over monoid rings $R[M]$, where $R$ is a
Externí odkaz:
http://arxiv.org/abs/2410.07631
In this paper, we investigate the internal (finite) sum of submonoids of rank-$1$ torsion-free abelian groups. These submonoids, when not groups, are isomorphic to nontrivial submonoids of the nonnegative cone of $\mathbb Q$, known as Puiseux monoids
Externí odkaz:
http://arxiv.org/abs/2409.19198
Autor:
Bhardwaj, Om Prakash
For a reduced one-dimensional complete local $k$-algebra $R$, Huneke et al. (Res. Math. Sci., 8(4), paper no. 60, 2021) introduced an important invariant, the reduced type. In this article, we study the extremal behavior of reduced type of some speci
Externí odkaz:
http://arxiv.org/abs/2406.15923
We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion, we determin
Externí odkaz:
http://arxiv.org/abs/2406.05781
A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are stably finite. In other words, given any field $K$ and any surjunctive m
Externí odkaz:
http://arxiv.org/abs/2405.18287