The pseudo-equivalence of a block lower triangular matrix T = [Tij ] over a regular ring and its block diagonal matrix D(T ) = [Tii] is characterized in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiX − Y Tjj = Uij .

DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium Dedicated to the memory of KARIN GATERMANN Table 1: List of mathematical symbols C field of complex numbers R field of real numbers Z ring of integer numbers C[x] ring of polynomials with coefficients in the field of complex numbers I ideal I def, tor deformed toric ideal V (I) variety of an ideal V (I def, tor) variety ...

Matrix-producing carcinoma (MPC) is extremely rare. Limited reports have described the cytological aspects of MPC. Herein, we present 2 cases of MPC, both of which showed ring-enhancement on magnetic resonance imaging (MRI) and chondromyxoid matrix on cytological specimens. In these cases, the diagnosis of MPC was preoperatively suspected. Recognizing extracellular matrix as chondromyxoid matri...

Microelectromagnet devices, a ring trap and a matrix, were developed for the microscopic control of biological systems. The ring trap is a circular Au wire with an insulator on top. The matrix has two arrays of straight Au wires, one array perpendicular to the other, that are separated and topped by insulating layers. Microelectromagnets can produce strong magnetic fields to stably manipulate m...

Adherence measurement for microbicide use within the clinical trial setting remains a challenge for the HIV prevention field. This paper describes an assay method used for determining residual dapivirine levels in post-use vaginal rings from clinical trials conducted with the Dapivirine Vaginal Matrix Ring-004 developed by the International Partnership for Microbicides to prevent male to female...

We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.

A ring R is called right strong stably finite (r.ssf) if for all n ≥ 1, injective endomorphisms of R (n) R are essential. If R is an r.ssf ring and e is an idempotent of R such that eR is a retractable R-module, then eRe is an r.ssf ring. A direct product of rings is an r.ssf ring if and only if each factor is so. The R.ssf condition is investigated for formal triangular matrix rings. In partic...

The endomorphism ring of the group of all sequences of integers, the Baer-Specker group, is isomorphic to the ring of row finite infinite matrices over the integers. The product bases of that group are represented by the multiplicative group of invertible elements in that matrix ring. All products in the Baer-Specker group are characterized, and a lemma of László Fuchs regarding such products i...