A characterization of rational star languages generated by strong codes.
A construction of right groups from a connected groupoid.
A counter-example on *-embeddability into proper *-rings.
A new approach to orders in simple rings with minimal one-sided ideals.
A Note on Extensions of Bear and P.p.-rings
A note on locally inverse semigroup algebras.
A Note On Units And Divisors Of Zero In Group Rings
A semigroup approach to wreath-product extensions of Solomon's descent algebras.
Algèbres de demigroupes, quotients d'algebres de demigroupes finis.
An algebraic characterization of multiplicative semigroups of real valued functions.
An example of two von Neumann regular rings with nonisomorphic Monta equivalent multiplicative semigroups.
Applications of epigroups to graded ring theory.
Archimedean property of ordered semirings.
Betti numbers of monoid algebras. Applications to 2-dimensional torus imbeddings.
Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation
2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras. Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A! is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k {0, and z, t ∈ X is satisfied...
Biordered sets and complemented modular lattices.
Centers of semigroup rings and conjugacy classes.
Combinatoric of syzygies for semigroup algebras.
We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.
Commutative semigroup rings which are principal ideal rings
Construction of set theoretic complete intersections via semigroup gluing.