Given a TQFT in dimension d + 1, and an infinite cyclic covering of a closed (d + 1)-dimensional manifold M , we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams’ work in symbolic dynamics. The Turaev-Viro module associated to a TQFT and an infinite cyclic covering is then given by the Jordan form...

Let k[G] be the group algebra, where G is a finite abelian p-group and k is a field of characteristic p. A complete classification of finitely generated k[G]-modules is available only when G is cyclic, Cpn , or C2 × C2. Tackling the first interesting case, namely modules over k[C2 × C4], some structure theorems revealing the differences between elementary and non-elementary abelian group cases ...

1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal. What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M is strictly cyclic if there exists m in M such that mA = M (such an m is called a generator); a r...

Index theory has had profound impact on many branches of mathematics. In this note we discuss the context for a new kind of index theorem. We begin, however, with some operator-theoretic results. In [11] Berger and Shaw established that finitely cyclic hyponormal operators have trace-class self-commutators. In [9], [31] Berger and Voiculescu extended this result to operators whose self-commutat...

Let A be a nondegenerate dimer (or ghor) algebra on torus, and let Z its center. Using cyclic contractions, we show the following are equivalent: is noetherian; noncommutative crepant resolution; each arrow of contained in perfect matching whose complement supports simple module; vertex corner rings eiAei pairwise isomorphic.

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...