Lectures on Commutative Algebra
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Three Lectures on Quasideterminants
Robert Lee Wilson Department of Mathematics Rutgers University The determinant of a matrix with entries in a commutative ring is a main organizing tool in commutative algebra. In these lectures, we present an analogous theory, the theory of quasideterminants, for matrices with entries in a not necessarily commutative ring. The theory of quasideterminants was originated by I. Gelfand and V. Retakh.
متن کاملCommutative pseudo BE-algebras
The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...
متن کاملLectures in Geometric Combinatorics
The fourteen lectures in this book were prepared for the advanced undergraduate course at the Park City Mathematics Institute on Geometric Combinatorics in July 2004. They begin with the basics of polytope theory with an emphasis on geometry via the theory of Schlegel and Gale diagrams. The lectures lead up to secondary and state polytopes arising from point configurations. These polytopes are ...
متن کاملPolynomial Systems and some Applications to Statistics
In the first part of my lectures we study systems of polynomial equations from the point of view of Gröbner bases. In the second part we introduce problems from Design of Experiments, a branch of Statistics, and show how to use Computational Commutative Algebra to solve some of them. Information about the computer algebra system CoCoA can be found at the URL http://cocoa.dima.unige.it/ The fund...
متن کاملAndré-Quillen homology of commutative algebras
These notes are an introduction to basic properties of AndréQuillen homology for commutative algebras. They are an expanded version of my lectures at the summer school: Interactions between homotopy theory and algebra, University of Chicago, 26th July 6th August, 2004. The aim is to give fairly complete proofs of characterizations of smooth homomorphisms and of locally complete intersection hom...
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تاریخ انتشار 2006