in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

Abstract This paper develops a theory of footing in Harmonic Serialism (HS; Prince & Smolensky 1993/2004; McCarthy 2000, 2016) where Con contains only directionally evaluated constraints (Eisner 2002; Lamont 2019, 2022 , b ). Directional harmonically order candidates by the location violations rather than total number violations. A central result adopting directional evaluation is that cons...

let $f: arightarrow b$ be a ring homomorphism and let $j$ be an ideal of $b$. in this paper, we investigate the transfer of the property of coherence to the amalgamation $abowtie^{f}j$. we provide necessary and sufficient conditions for $abowtie^{f}j$ to be a coherent ring.

Lambek’s unified classification of the elementary interaction-quanta of the “Standard model” is formulated in terms of the 24 units of the integerquaternion ring, i.e., the tetrahedral group Q24. An extension of Lambek’s scheme to the octahedral group Q48 may enable to take all three generations of leptons and quarks into account, as well as to provide a quantitative explanation for flavor-mixi...

Our understanding of the cycling of fire-derived, i.e., pyrogenic organic matter (pyOM), as well as the goals of the community of researchers who study it, may be inhibited by the many terms and methods currently used in its quantification and characterization. Terms currently used for pyOM have evolved by convention, but are often poorly defined. Further, each of the different methods now used...

Hebbian and competitive Hebbian algorithms are almost ubiquitous in modeling pattern formation in cortical development. We analyse in theoretical detail a particular model (adapted from Piepenbrock & Obermayer, 1999) for the development of Id stripe-like patterns, which places competitive and interactive cortical influences, and free and restricted initial arborisation onto a common footing.