We show that the right ideal of a Novikov algebra generated by square nilpotent subalgebra is nilpotent. also prove [Formula: see text]-graded text] over field with solvable text]-component solvable, where finite additive abelean group and characteristic does not divide order text]. any automorphisms if invariants solvable.

We characterize the edge versus path incidence matrix of a series-parallel graph. One characterization is algorithmic while the second is structural. The structural characterization implies that the greedy algorithm solves the max 7ow problem in series-parallel graphs, as shown by Bein et al. (Discrete Appl. Math. 10 (1985) 117–124). The algorithmic characterization gives an e8cient way to iden...

Bandelt and Mulder’s structural characterization of Bipartite Distance Hereditary graphs asserts that such graphs can be built inductively starting from a single vertex and by repeatedly adding either pending vertices or twins (i.e., vertices with the same neighborhood as an existing one). Dirac and Duffin’s structural characterization of 2–connected series–parallel graphs asserts that such gra...

For each sequence P = (p1(t), p2(t), . . . ) of polynomials we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S, such a sequence of polynomials arises naturally as the orders of certain submodules of a sequence of higher-order Alexander modules of K. These group series yield filtrations of the knot concordance group that refine the (n)-solv...

The Steiner Subgraph Problem (PS for short) is a natural generalization of the classical Steiner Tree Problem. Instead of only one terminal net there is given a set of terminal nets. The task is to choose a susbet F of edges at minimum cost such that vertices of the same net lie in the same connected component in the graph induced by F . Richey and Parker [7] posed the question whether PS is ha...