Emilia, Alonso M. Thierry, Coquand Henri, Lombardi

This paper deals with the Peskine version of Zariski Main Theorem published in 1965 and discusses some applications. It is written in the style of Bishop's constructive mathematics. Being constructive, each proof in this paper can be interpreted as an algorithm for constructing explicitly the conclusion from the hypothesis. The main non-constructiv...

Kornev, Alexandr

We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated ...

Himstedt, Frank Symonds, Peter

We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.

Stark, Jim

We explicitly compute examples of sheaves over the projectivization of the spectrum of the cohomology of sl_2. In particular, we compute \ker\Theta_M for every indecomposable M and we compute F_i(M) when M is an indecomposable Weyl module and i \neq p. We also give a brief review of the classification of sl_2-modules and of the general theory of su...

Alahmadi, Adel Jain, Surender Leroy, André

In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey ( Products of idempotent matrices. Linear Multilinear A. 1983) and Rao (Products of idempotent matrices. Li...

Kauta, John S.

Let $F$ be a field, let $V$ be a valuation ring of $F$ of arbitrary Krull dimension (rank), let $K$ be a finite Galois extension of $F$ with group $G$, and let $S$ be the integral closure of $V$ in $K$. Let $f:G\times G\mapsto K\setminus \{0\}$ be a normalized two-cocycle such that $f(G\times G)\subseteq S\setminus \{0\}$, but we do not require tha...

Fryer, Siân

We prove that the fixed ring of the $q$-division ring $k_q(x,y)$ under any finite group of monomial automorphisms is isomorphic to $k_q(x,y)$ for the same $q$. In a similar manner, we also show that this phenomenon extends to an automorphism that is defined only on $k_q(x,y)$ and does not restrict to $k_q[x^{\pm1},y^{\pm1}]$. We then use these resu...

Nakashima, Norihiro Tsujie, Shuhei

A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value property for polytopes. In this article, we naturally identify the vector space spanned by a canonical system of basic invariants with an invariant space determined by a fund...

Cooper, Susan M. Hartke, Stephen G.

Motivated by the work of Chudnovsky and the Eisenbud-Mazur Conjecture on evolutions, Harbourne and Huneke give a series of conjectures that relate symbolic and regular powers of ideals of fat points in $\mathbb P^n$. The conjectures involve both containment statements and bounds for the initial degree in which there is a non-zero form in an ideal. ...

Gray, Robert Ruskuc, Nik

In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M; (RFSG) residual finiteness of Schutzenberger groups of M; and (RFRL) residual finiteness of the natural actions of M on its Green's R- and L-classes. The general question is whether (RFM) implies (RFSG) and/or (RFRL), and vice versa. We c...