Showing papers on "Ring (mathematics) published in 2022"
TL;DR: In this article, a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of simplicial affine semiigroups is presented. But the authors do not define the type of S, type (S ), in terms of some Apery sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when K [ S ] is Cohen-MACaulay.
8 citations
TL;DR: This paper proposes the first logarithmic-size repudiable ring signature scheme, which means the size of signatures and repudiations grows onlyLogarithmically in the ring size, and presents a new requirement (repudiation-unforgeability), which requires ‘no one can forge a valid repudiation’.
5 citations
TL;DR: The quantum Frobenius Heisenberg category was introduced in this article, which is a generalization of the affine HOMFLY-PT skein category for morphism spaces.
4 citations
TL;DR: In this article, the authors gave necessary and sufficient conditions under which the Leavitt path algebra of an ultragraph over a field K is purely infinite simple and that it is von Neumann regular.
Abstract: In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$
of an ultragraph $$\mathcal {G}$$
over a field K is purely infinite simple and that it is von Neumann regular. Consequently, we obtain that every graded simple ultragraph Leavitt path algebra is either a locally matricial algebra, or a full matrix ring over $$K[x, x^{-1}]$$
, or a purely infinite simple algebra.
3 citations
TL;DR: In this article, it was shown that negative curves are rational in many cases and that the Cox ring of the blow-up of a toric variety at the point (1, 1, 1, …, 1 ) coincides with the extended symbolic Rees ring of an ideal of a polynomial ring.
2 citations
TL;DR: In this paper, the existence of the HK density function for a graded pair (R, I ) is proved for the case where R is an N -graded domain of finite type over a perfect field and I ⊂ R is a graded ideal of finite colength.
2 citations
TL;DR: In this article, the minimal number of separating invariants for the invariant ring of a matrix group G ≤ GL n (F q ) over the finite field F q can be obtained with invariants of degree |G | n ( q − 1 ).
2 citations
TL;DR: The concept of index and co-index of a paracompact Hausdorff space X equipped with free involutions relative to the antipodal action on spheres was introduced by Conner and Floyd.
2 citations
TL;DR: In this article, it was shown that a 1-tilting cotorsion pair over a commutative ring is enveloping if and only if G is a perfect Gabriel topology (that is, it arises from a perfect localisation).
2 citations
TL;DR: In this paper, it was shown that the bivariant algebraic algebraic cobordism groups considered previously by the author are independent of the chosen base ring $A$.
1 citations
TL;DR: In particular, it is not possible to prove (unless Vopěnka's Principle is inconsistent) that there is a ring over which the Ding Projectives or the Gorenstein Projectives do not form a precovering class as discussed by the authors.
TL;DR: In this paper, it was shown that every element in the boundary of the group of invertibles of a complete almost absolutely semi-normed ring is a topological zero divisor.
Abstract: Every element in the boundary of the group of invertibles of a Banach algebra is a topological zero divisor. We extend this result to the scope of topological rings. In particular, we define a new class of semi-normed rings, called almost absolutely semi-normed rings, which strictly includes the class of absolutely semi-valued rings, and prove that every element in the boundary of the group of invertibles of a complete almost absolutely semi-normed ring is a topological zero divisor. To achieve all these, we have to previously entail an exhaustive study of topological divisors of zero in topological rings. In addition, it is also well known that the group of invertibles is open and the inversion map is continuous and $$\mathbb {C}$$
-differentiable in a Banach algebra. We also extend these results to the setting of complete normed rings. Finally, this study allows us to generalize the point, continuous and residual spectra to the scope of Banach algebras.
TL;DR: In this paper, the relative dominant dimension of projective Noetherian algebras is investigated and a relative version of the Morita-Tachikawa correspondence is established.
TL;DR: In this paper, Herzog and Hibi generalize their result to polymatroids that are products of polymatros with the strong exchange property and show that the conjecture holds for polymatroids with the so-called strong exchange properties.
TL;DR: In this article, the behavior of ideal-adic separatedness and completeness under certain ring extensions using trace map is examined, and it is shown that adic completeness of a base ring is hereditary to its ring extension under reasonable conditions.
TL;DR: In this article, the authors studied the action of G by matrix right-multiplication on V n (M ), the set of elements of M n whose components generate M. Assuming that M is finitely presented and that R is an elementary divisor ring or an almost local-global coherent Prufer ring, they obtained a description of V n(M ) / G which extends the author's earlier result on finitely generated modules over quasi-Euclidean rings.
TL;DR: Campanini, El-Deken and Facchini as mentioned in this paper consider a small category naturally associated with any fixed R-S-bimodule M S R and show that the class of objects of this category is the underlying set M of M S r.
TL;DR: In this article, the authors studied the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition and gave a parametrization by rational functions.
TL;DR: In this paper, the authors studied Bruhat generation over commutative and non-commutative local and adelic rings R and proved that A is ⁎-Euclidean and explored reduction modulo the Jacobson radical for such rings.
01 Jan 2022
TL;DR: In this article, a parametrization of the integral solutions of the equation $x^2+3y^2=12n+4, where n is a positive integer, using the 3-core partitions of n is presented.
Abstract: This note is concerned with the set of integral solutions of the equation $x^2+3y^2=12n+4$, where $n$ is a positive integer. We will describe a parametrization of this set using the 3-core partitions of n. In particular we construct a crank using the action of a suitable subgroup of the isometric group of the plane that we connect with the unit group of the ring of Eisenstein integers. We also show that the process goes in the reverse direction: from the solutions of the equation and the crank, we can describe the 3-core partitions of n. As a consequence we describe an explicit bijection between $3$-core partitions and ideals of the ring of Eisenstein integers, explaining a result of G. Han and K. Ono obtained using modular forms.
01 Jan 2022
TL;DR: In this paper, the average p r -dimension of the Euclidean hull of a cyclic serial code over a finite chain ring was established, and an algorithm for computing all the possible parameters of the hulls of that code was presented.