Related papers: Simultaneous Monomialization

Let $R$ be a finite ring and let $M, N$ be two finite left $R$-modules. We present two distinct deterministic algorithms that decide in polynomial time whether or not $M$ and $N$ are isomorphic, and if they are, exhibit an isomorphism. As…

The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of…

We develop a theory of formal multivariate polynomials over commutative rings by treating them as ring terms. Our main result is that two ring terms are s-equivalent (when expanded they yield the same standard polynomial) iff they are…

In this work we prove the undecidability (and $\Sigma^0_1$-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective…

The aim of this paper is sketch a theory of divisibility and factorisation in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely…

Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…

We study the quasi-endomorphism ring of infinitely definable subgroups in separably closed fields. Based on the results we obtain, we are able to prove a Mordell-Lang theorem for Drinfeld modules of finite characteristic. Using…

We study a question raised by Eisenbud, Mustata, and Stillman regarding the injectivity of natural maps from Ext modules to local cohomology modules. We obtain some positive answers to this question which extend earlier results of…

This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…

An algorithmic proof of General Neron Desingularization is given here for one dimensional local rings and it is implemented in Singular. Also a theorem recalling Greenberg' strong approximation theorem is presented for one dimensional local…

We study local equivalence of bounded complexes over a polynomial ring $R[w]$, where $R$ is a noetherian ring. We provide a homological algebra approach to the results, the variants of which have been proved in many places in the…

We identify quotient polynomial rings isomorphic to the recently found fundamental fusion algebras of logarithmic minimal models.

We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a…

We prove that a local ring $R$ of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, $R$ itself and a dualizing $R$-complex if one exists.

We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and…

In this paper we introduce a model theoretic construction for the theories of uniform layered domains and semifields introduced in the paper of Izhakian, Knebusch and Rowen. We prove that, for a given layering semiring L, the theory of…

Let $A$ be a commutative Noetherian ring containing a field of characteristic zero. Let $R= A[X_1, \ldots, X_m]$ be a polynomial ring and $A_m(A) = A \langle X_1, \ldots, X_m, \partial_1, \ldots, \partial_m \rangle$ be the $m^{th}$ Weyl…

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). A theorem of Lipman implies that I has a unique factorization as a *-product of special *-simple complete ideals with possibly negative exponents for…

In this paper, we introduce and investigate a new notion of exact sequences of semimodules over semirings relative to the canonical image factorization. Several homological results are proved using the new notion of exactness including some…

In recent years, centrally essential rings have been intensively studied in ring theory. In particular, they find applications in homological algebra, group rings, and the structural theory of rings. The class of essentially central rings…