In this note we obtain a necessary and sufficient condition for a ring to be -weakly regular (i) When is a ring with identity and without divisors of zero (ii) When is a ring without divisors of zero. Further it is proved in a -weakly regular ring with identity and without units every element is a zero divisor.
In questo lavoro studiamo i non CC-gruppi monolitici con tutti i quozienti propri CC-gruppi, che hanno sottogruppi abeliani normali non banali.
We define the singular Hecke algebra as the quotient of the singular braid monoid algebra by the Hecke relations , . We define the notion of Markov trace in this context, fixing the number of singular points, and we prove that a Markov trace determines an invariant on the links with singular points which satisfies some skein relation. Let denote the set of Markov traces with singular points. This is a -vector space. Our main result is that is of dimension . This result is completed...
We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2,C)-representations of G. We also solve, for abelian groups, the conjecture of Bullock on SL(2,C) character varieties of groups - we show...
MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).