Wen-Fong Ke

GRÖBNER-SHIRSHOV BASES FOR THE BRAID SEMIGROUP

We found Groebner-Shirshov basis for the braid semigroup

On skew-symmetric maps on Lie algebras

B^+_{n+1}

Zero product preserving maps of operator-valued functions

. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group.

An example of a rightq-ring

For certain Lie subalgebras L of associative algebras Q , we characterize the multi-additive skew-symmetric maps f : L n → Q , which are covariant under the action of L .

On maps preserving products

Let X, Y be locally compact Hausdorff spaces and M, N be Banach algebras. Let θ: C 0 (X,M) → C 0 (Y,N) be a zero product preserving bounded linear map with dense range. We show that θ is given by a continuous field of algebra homomorphisms from M into N if N is irreducible. As corollaries, such a surjective θ arises from an algebra homomorphism, provided that M is a W*-algebra and N is a semi-simple Banach algebra, or both M and N are C*-algebras.

Combinatorial properties of ring generated circular planar nearrings

We show that Ivanov’s classification of indecomposable non-local rightq-rings is incomplete and provide a complete classification. Next, we correct and sharpen Byrd’s classification of rightq-rings.

A Note on Polynomial Rings over Nil Rings

Maps preserving certain algebraic properties of elements are often studied in Functional Analysis and Linear Algebra. The goal of this paper is to discuss the relationships among these problems from the ring-theoretic point of view.

On graded polynomial identities with an antiautomorphism

for all a, b ~ C. The incidence structure obtained from this planar nearring is (C, ~* , ~), where T is the unit circle and ~ * is the set of all circles in the complex plane. To initialize the study, Clay chooses the family of circles in ~ * with a fixed radius r, r :/: 0, and then partitions this family into equivalence classes E~ = { Tr + b I b ~ Tc}, where c :/: 0. Each E~ is the family of circles with radius r and centers on the circle Tc. Then a graph is assigned to each E~ in order to understand the behavior of E~ (cf. I-4; §6]). This idea has been proven to be very useful. In this work, we continue the study of these E~s for circular planar nearrings constructed from a ring using a cyclic subgroup of order k of the

Nonexistence of derivations on transformation near-rings

Let R be a nil ring with p R = 0 for some prime number p. We show that the polynomial ring R[x,y] in two commuting indeterminates x, y over R cannot be homomorphically mapped onto a ring with identity. This extends, in finite characteristic case, a result obtained by Smoktunowicz [8] and gives a new approximation, in that case, of a positive solution of Kothe’s problem.

A linear algebra approach to Koethe's problem and related questions

Let G be a commutative monoid with cancellation and let R be a strongly G-graded associative algebra with finite G-grading and with antiautomorphism. Suppose that R satisfies a graded polynomial identity with antiautomorphism. We show that R is a PI algebra.