let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We apply the method of Arzhantseva-Ol’shanskii to prove that for an exponentially generic (in the sense of Ol’shanskii) class of one-relator groups the isomorphism problem is solvable in at most exponential time. This is obtained as a corollary of the more general result that for any fixed integers m > 1, n > 0 there is an exponentially generic class of m-generator n-relator groups where every ...

In this paper we study an open problem: Is it true that each homotopy domination of a polyhedron over itself is equivalence? Since every ANR has the type polyhedron, question related in obvious way to longstanding Borsuk's problem (1967) two ANR's dominating other have same type? The answer positive for all polyhedra (or ANR's) with polycyclic-by-finite fundamental groups, manifolds, and clearl...