Статтіhttp://hdl.handle.net/123456789/552024-06-17T07:14:41Z2024-06-17T07:14:41ZOn large indecomposable modules, endo-wild representation type and right pure semisimple ringsSimson, Danielhttp://hdl.handle.net/123456789/622020-01-24T21:27:37Z2003-03-24T00:00:00ZOn 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
2003-03-24T00:00:00ZOn the representation of a number as a sum of the k-th powers in an arithmetic progressionProsyanyuk, N.S.http://hdl.handle.net/123456789/612020-01-24T21:27:01Z2003-02-27T00:00:00ZOn 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.
2003-02-27T00:00:00ZTiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. IIChernousova, Zh.T.Dokuchaev, M.A.Khibina, M.A.Kirichenko, V.V.Miroshnichenko, S.G.Zhuravlev, V.N.http://hdl.handle.net/123456789/602020-01-24T21:25:01Z2003-03-28T00:00:00ZTiled 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.
2003-03-28T00:00:00ZFlows in graphs and the homology of free categoriesHusainov, Ahmet A.Çalisici, Hamzahttp://hdl.handle.net/123456789/592020-01-24T21:27:36Z2003-05-13T00:00:00ZFlows 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