Related papers: A commutative version of the group ring
It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years. In this survey article we discuss some of the…
We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…
A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional…
I provide several natural properties of group actions which translate into fragments of axiom of choice in the associated permutation models of choiceless set theory.
With an arbitrary finite graph having a special form of 2-intervals (a diamond-shaped graph) we associate a subgroup of a symmetric group and a representation of this subgroup; state a series of problems on such groups and their…
Let $R$ be a commutative ring with a collection of ideals $\{ N_1, N_2, \dots, N_{k-1}\}$ satisfying certain conditions, properties of the set of invertible quadratic residues of the ring $R$ are described in terms of properties of the set…
Given a monomial ideal in a polynomial ring over a field, we define the generalized Newton complementary dual of the given ideal. We show good properties of such duals including linear quotients and isomorphisms between the special fiber…
We prove a normality theorem for the "true" elementary subgroups of $SL_n(A)$ defined by the ideals of a commutative unital ring $A$. Our result is an analogue of a normality theorem, due to Suslin, for the standard elementary subgroups,…
Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduce and investigate the dual notion of morphic modules over a commutative ring.
Let F be a field and A a free associative F-algebra or a group algebra of a free group with an infinite set X of generators. We find a necessary and sufficient condition for the inclusion I' into I, where I=I_1...I_k and I'=I'_1...I'_l are…
In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it…
In this paper, we shall give an explicit proof that constacyclic codes over finite commutative rings can be realized as ideals in some twisted group rings. Also, we shall study isometries between those codes and, finally, we shall study…
We characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring $A$ is bi-interpretable with $(\mathbb N,{+},{\times})$ if and only if the space…
We describe an efficient algorithm to write any element of the alternating group A_n as a product of two n-cycles (in particular, we show that any element of A_n can be so written -- a result of E. A. Bertram). An easy corollary is that…
We give a new and self-contained proof of the finite generation of adjoint rings with big boundaries. As a consequence, we show that the canonical ring of a smooth projective variety is finitely generated.
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…
Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
The support of any module over a commutative ring is defined as the collection of all prime ideals of the ring at which the localization of the module is non-zero. For finitely generated modules, the support is the collection of all prime…
We show that the class of amalgamated free products of two free groups over a cyclic subgroup admits amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free…