arXiv subjects

Alexander J. Diesl

Publications and source records attributed to Alexander J. Diesl.

3 recordsLinked to original sources

arXiv2026

Class-uniformly resolvable designs with all but one block having size two

A Class-Uniformly Resolvable Design (CURD) is a resolvable design in which each parallel class has the same block structure. We study CURDS in which each parallel class contains one block of size $m$ and the remaining blocks have size $2$, for $m \ge 3$. In addition to establishing necessary conditions for such a CURD to exist, we present two general constructions. The first transforms a particular type of cyclic design with block size $k$ into a CURD with partition $m^12^{\frac{n-m}{2}}$ where $m = 2k$. This construction is used to generate CURDS with 26 varieties (where $m=6$) and with 82 varieties (where $m=10$). The second constructs a CURD with partition $m^12^{\frac{n-m}{2}}$ for every value of $m$ that is the power of an odd prime.

math.CO↗

arXiv2009

A note on completeness in the theory of strongly clean rings

Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we prove that if $R$ is a ring which is complete with respect to an ideal $I$ and if $x$ is an element of $R$ whose image in $R/I$ is strongly $π$-regular, then $x$ is strongly clean in $R$.

math.RA↗

arXiv2009

A Characterization of Certain Morphic Trivial Extensions

Given a ring $R$, we study the bimodules $M$ for which the trivial extension $R\propto M$ is morphic. We obtain a complete characterization in the case where $R$ is left perfect, and we prove that $R\propto Q/R$ is morphic when $R$ is a commutative reduced ring with classical ring of quotients $Q$. We also extend some known results concerning the connection between morphic rings and unit regular rings.

math.RA↗