In their paper [1], H. Ananthnarayan, L. Avramov, and W.F. Moore introduced a connected sum construction for local Gorenstein rings A,B over ring T, which, in the graded Artinian case, can be viewed as an algebraic analogue of topological same name. We give two alternative descriptions this sum: first uses analogues Thom classes vector bundles Gysin homomorphisms, second is terms Macaulay dual ...

In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete fields K 1 and 2 with perfect residue fields, show that if n -th rings are isomorphic for each ? , then isometric isomorphic. More generally, there is depending only on ramification indices such homomorphism from ring to can be lifted a between valuation rings. Moreover...

‎let $i$ be an ideal in a regular local ring $(r,n)$‎, ‎we will find‎ ‎bounds on the first and the last betti numbers of‎ ‎$(a,m)=(r/i,n/i)$‎. ‎if $a$ is an artinian ring of the embedding‎ ‎codimension $h$‎, ‎$i$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $a$ a {it $t-$extended stretched local ring}‎. ‎this class of‎ ‎local rings is a natural generalization of the class of stretched ...

Let (S,≤) be a strictly totally ordered monoid, R be a commutative ring and M be an R-module. We show the following results: (1) If (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a semi Hopfian [[RS,≤]]-module if and only if M is a semi Hopfian R-module; (2) If (S,≤) is artinian, then the generalized inverse polynomial module [MS,...

We consider various conditions of the sets of zero-dimensional, Artinian, and von Neumann regular subrings of a commutative ring. Section 1 treats questions of existence of such rings, Section 2 deals with the situation in which all subrings belong to one of the three classes, and Section 3 is concerned with the behavior of the sets under intersection. In Section 4 we give a brief survey of som...

Let [Formula: see text] be a commutative Noetherian ring. For finitely generated text]-module text], Northcott introduced the reducibility index of which is number submodules appearing in an irredundant irreducible decomposition submodule text]. On other hand, for Artinian Macdonald proved that sum-irreducible representation does not depend on choice representation. This called sum-reducibility...

Let R be a ring and M a right R-module. It is shown that: (1) M is Artinian if and only if M is a GAS-module and satisfies DCC on generalized supplement submodules and on small submodules; (2) if M satisfies ACC on small submodules, then M is a lifting module if and only if M is a GASmodule and every generalized supplement submodule is a direct summand of M if and only if M satisfies (P ∗); (3)...

We describe an algorithm that computes explicit models of hyperelliptic Shimura curves attached to an indefinite quaternion algebra over Q and Atkin-Lehner quotients of them. It exploits Cerednik-Drinfeld’s nonarchimedean uniformisation of Shimura curves, a formula of Gross and Zagier for the endomorphism ring of Heegner points over Artinian rings and the connection between Ribet’s bimodules an...

Group automata occur in the Krohn-Rhodes Decomposition Theorem and have been extensively investigated in the literature. The incidence rings of group automata were introduced by the first author in analogy with group rings and incidence rings of graphs. The main theorem of the present paper gives a complete description of the structure of incidence rings of group automata in terms of matrix rin...

Goldie’s Theorem (1960), which is one of the most important results in Ring Theory, is a criterion for a ring to have a semisimple left quotient ring. The aim of the paper is to give four new criteria (using a completely different approach and new ideas). The first one is based on the recent fact that for an arbitrary ring R the set M of maximal left denominator sets of R is a non-empty set [2]...