http://hdl.handle.net/123456789/39 2026-04-16T00:14:35Z http://hdl.handle.net/123456789/62 On large indecomposable modules, endo-wild representation type and right pure semisimple rings Simson, Daniel The existence of large indecomposable right Rmodules over a right artinian ring R is discussed in connection with the pure semisimplicity problem and the endo-wildness of the category Mod(R) of right R-modules. Some conjectures and open problems are presented 2003-03-24T00:00:00Z http://hdl.handle.net/123456789/61 On the representation of a number as a sum of the k-th powers in an arithmetic progression Prosyanyuk, N.S. In this paper we obtain the asymptotic formula for a natural n 6 x which representate as a sum of two non-negative k-th powers in an arithmetic progression. 2003-02-27T00:00:00Z http://hdl.handle.net/123456789/60 Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II Chernousova, Zh.T.; Dokuchaev, M.A.; Khibina, M.A.; Kirichenko, V.V.; Miroshnichenko, S.G.; Zhuravlev, V.N. The main concept of this part of the paper is that of a reduced exponent matrix and its quiver, which is strongly connected and simply laced. We give the description of quivers of reduced Gorenstein exponent matrices whose number s of vertices is at most 7. For 2 6 s 6 5 we have that all adjacency matrices of such quivers are multiples of doubly stochastic matrices. We prove that for any permutation σ on n letters without fixed elements there exists a reduced Gorenstein tiled order ¤ with σ(E) = σ. We show that for any positive integer k there exists a Gorenstein tiled order ¤k with in¤k = k. The adjacency matrix of any cyclic Gorenstein order ¤ is a linear combination of powers of a permutation matrix P¾ with non-negative coefficients, where σ = σ(¤). If A is a noetherian prime semiperfect semidistributive ring of a finite global dimension, then Q(A) be a strongly connected simply laced quiver which has no loops. 2003-03-28T00:00:00Z http://hdl.handle.net/123456789/59 Flows in graphs and the homology of free categories Husainov, Ahmet A.; Çalisici, Hamza We study the R−module of generalized flows in a graph with coefficients in the R−representation of the graph over a ring R with 1 and show that this R−module is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff’s laws and build an exact sequence for calculating the R−module of flows in the union of graphs. 2003-05-13T00:00:00Z