‎Let $mathcal A$ and $mathcal B$ be unital rings‎, ‎and $mathcal M$‎ ‎be an $(mathcal A‎, ‎mathcal B)$-bimodule‎, ‎which is faithful as a‎ ‎left $mathcal A$-module and also as a right $mathcal B$-module‎. ‎Let ${mathcal U}=mbox{rm Tri}(mathcal A‎, ‎mathcal M‎, ‎mathcal‎ ‎B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its‎ ‎center‎. ‎Assume that $f:{mathcal U}rightarrow{mathcal U}$ is...

This paper aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving a finite group Γ acting on a regular triangular algebra A. We develop Clifford theory for A⋊Γ, and obtain results on block decomposition, complete r...

The title complex, [Ag3Br2(C25H22P2)3]Br·C7H8N2S, comprises a trinuclear [Ag3Br2(C25H22P2)3](+) unit, a Br(-) anion and one N,N'-di-methyl-thio-urea mol-ecule (ptu). Three Ag(I) ions are linked via two μ3-bridging Br atoms, leading to a distorted triangular bipyramid with an Ag⋯Ag separation range of 3.1046 (6)-3.3556 (6) Å. The triangular Ag3 arrangement is stabilized by six P atoms from three...

The classes of clean and nil-clean rings are closed with respect standard constructions as direct products and (triangular) matrix rings, cf. [12] resp. [4], while the classes of weakly (nil-)clean rings are not closed under these constructions. Moreover, while all matrix rings over fields are clean, [12] when we consider nil-clean rings there are strongly restrictions: if a matrix ring over a ...

We present a scheme to categorize the structure of different layered phosphorene allotropes by mapping their nonplanar atomic structure onto a two-color 2D triangular tiling pattern. In the buckled structure of a phosphorene monolayer, we assign atoms in "top" positions to dark tiles and atoms in "bottom" positions to light tiles. Optimum sp3 bonding is maintained throughout the structure when ...

The self-assembly of well-defined 2D supramolecular polymers in solution has been a challenge in supramolecular chemistry. We have designed and synthesized a rigid stacking-forbidden 1,3,5-triphenylbenzene compound that bears three 4,4'-bipyridin-1-ium (BP) units on the peripheral benzene rings. Three hydrophilic bis(2-hydroxyethyl)carbamoyl groups are introduced to the central benzene ring to ...

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...