Syzygies of Cohen–Macaulay Modules over One Dimensional Cohen–Macaulay Local Rings

Algebras and Representation Theory - We study syzygies of (maximal) Cohen–Macaulay modules over one dimensional Cohen–Macaulay local rings. We assume that rings are generically...     

Structure of algebras

Weakenings of the L and P-properties are considered. It ib shown that if semigroups, rings, or Lie Algebras of matrices have certain of these properties, then they are triangular. In particular the result of Zassenhaus on L-semigroups is generalized. Also, Lie Algebras over a field of characteristic 0 which have the L-property are triangular.     

Morita Invariance for Infinitesimal Deformations

Algebras and Representation Theory - Let A and B be two Morita equivalent finite dimensional associative algebras over a field ��. It is well known that Hochschild cohomology is...     

Generic Constructions and Semidualizing Modules

Algebras and Representation Theory - We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a...     

Auslander-Reiten Conjecture in a Dual Vein

Algebras and Representation Theory - We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian algebras over commutative Noetherian rings. Firstly, in the...     

关于内结合环的注记（英）

ＩｎｎｅｒＡｓｏｃｉａｔｉｖｅＲｉｎｇｓＷ．Ｂ．ＶａｓａｎｔｈａＫａｎｄａｓａｍｙ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＩｎｄｉａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙＭａｄｒａｓ－６０００３６，Ｉｎｄｉａ）ＡｂｓｔｒａｃｔＩｎｆｌｕｅｎｃｅｄｂｙｔｈ...     

The Minimal Polynomial of Some Matrices Via Quaternions

This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete determination of the Jordan structure of skew-Hamiltonian matrices and the computation of the Cayley transform are given. Some new classes of matrices are uncovered, whose behaviour insofar as minimal polynomials are concerned, is remarkably similar to those of skew-Hamiltonian and Hamiltonian matrices. The main technique is the invocation of the associative algebra isomorphism between the tensor product of the quaternions with themselves and the algebra of real 4 × 4 matrices. Extensions to higher dimensions via Clifford Algebras are discussed.     

COMMUTATIVE ALTERNATIVE RINGS: A CONSTRUCTION

In this paper, the authors establish a connection between commutative, alternative rings and Engel rings(of type 2), thereby providing a method for constructing commutative, alternative rings which are not associative.     

cu-条件的Morita不变性

本文证明了ｒｃ－条件下的ｃｕ－条件是Ｍｏｒｉｔａ不变的．     

Linearly ordered rings which are not o-epimorphic images of ordered free rings

A proof is given that not every linearly ordered associative (associative-commutative) ring is the o-image of a free associative (associative-commutative) ring for some ordering of the latter. There are also nilpotent linearly ordered rings which are not o-epimorphic images of free associative or free associative-commutative n-nilpotent rings for n 4, no matter what ordering is used for the latter.Translated from Matematicheskie Zametki, Vol. 9, No. 6, pp. 693–697, June, 1971.     

THE ADDITIVE GROUPS OF RINGS WITH TOTALLY ORDERED LATTICE OF IDEALS

The object of this paper is to describe the additive groups of rings R satisfying the following condition: For any two ideals A,B in R either A u B, or B u A. Such rings will be called TOLI rings. The rings considered here are not necessarily associative or with identity.     

Elementary equivalence of rings with finitely generated additive groups

We give algebraic characterizations of elementary equivalence between rings with finitely generated additive groups. They are similar to those previously obtained for finitely generated nilpotent groups. Here, the rings are not supposed associative, commutative or unitary.     

Alternative rings of small order

We construct all the alternative (but not associative) algebras of dimension at most 5 over a perfect field. For any prime p, we show that there are fifteen alternative rings of prime power order pⁿ ,n≤5, which are not associative. None of these rings is nil. Just one has a unity.     

Descent constructions for central extensions of infinite dimensional Lie algebras

We use Galois descent to construct central extensions of twisted forms of split simple Lie algebras over rings. These types of algebras arise naturally in the construction of Extended Affine Lie Algebras. The construction also gives information about the structure of the group of automorphisms of such algebras. A. Pianzola is supported by the NSERC Discovery Grant Program. The author also wishes to thank the Instituto Argentino de Matemática for their hospitality. D. Prelat is supported by a Research Grant from Universidad CAECE.     

Elementary equivalence of the semigroup of invertible matrices with nonnegative elements

In this paper, we prove that the semigroups of invertible matrices with nonnegative elements over linearly ordered associative rings are elementarily equivalent if and only if the matrices have the same dimension and the rings are elementarily equivalent as ordered rings. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 39–53, 2006.     

Orderings of higher level on noetherian rings

The noncommutative algebraic geometry has found fruitful applications in quantum geometry. Similar applications are expected to be found for its younger sister the noncommutative real algebraic geometry

One of the basic results in real algebraic geometry is the Positivestellensatz. The original results of Dubois and Risler (see section 3.3 of [13]) have been extended in many directions. We refer to [14], [1], [2], [3] for commutative rings and [9], [4] for associative rings. The aim of this paper is to prove the higher level Posit ivstellensatz for noncommutative Noetherian rings. Our proof depends on the intersection theorem for orderings of higher level on skew fields ([11], Theorem 3.13). The general case of orderings of higher level on associative rings remains open.     

Structure of bicategorical structures

We prove that the totalities of bicategorical structures in categories of associative rings and topological spaces are not sets.