2008 NOV 24 - (VerticalNews.com) -- "Let k be an algebraically closed field of arbitrary characteristic," investigators in the United States report.

  "We give a self-contained algebraic proof of the following statement: If V is an affine surface over k such that V x k congruent to k(3), then V congruent to k(2). This fact, which is due to Fujita, Miyanishi, Sugie, and Russell, solves the Zariski cancellation problem for surfaces," wrote A.J. Crachiola and colleagues, Saginaw Valley State University ...read more

  2008 NOV 24 - (VerticalNews.com) -- 'The paper is devoted to finding a homomorphic image for the c-nilpotent multiplier of the verbal product of a family of groups with respect to a variety V when V subset of N-c or N-c subset of V. Also a structure of the c-nilpotent multiplier of a special case of the verbal product, the nilpotent product, of cyclic groups is given. In fact, we present an explicit formula for the c-nilpotent multiplier G = Z(*)(n)... (n)(*) Z(*)(n)Z(r1) (n)(*)... of the nth nilpotent product of the group (n)(*)Z(rt), where r(i+1) divides r(i) for all i, 1<= i<= t - 1, and (p, r(1)) = 1 for any prime p less than or equal to n + c, for all positive integers n, c ...read more

  2008 NOV 24 - (VerticalNews.com) -- "Consider a local chain Differential Graded algebra, such as the singular chain complex of a pathwise connected topological group. In two previous papers, a number of homological results were proved for such an algebra: An Amplitude Inequality an Auslander-Buchsbaum Equality and a Cap Theorem," scientists in the United Kingdom report.

  "These were inspired by homological ring theory. By the so-called looking glass principle, one would expect that analogous results exist for simply connected cochain Differential Graded algebras, such as the singular cochain complex of a simply connected topological space," wrote A.J. Frankild and colleagues, University of Newcastle ...read more