We develop the theory of special biserial and string coalgebras and other concepts from the representation theory of quivers. These theoretical tools are then used to describe the finite dimensional comodules and Auslander-Reiten quiver for the coordinate Hopf algebra of quantum SL(2) at a root of unity. We also describe the stable Green ring. Let C = k ζ [SL(2)] denote the quantized coordinate...

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

The effect of alkyl substituents on the C-phenyl and/or the N-Phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. The predominant configuration in CHCl3 is determined by steric and electronic effects. Substituents on the C-phenyl ring favor the cis configuration, while substituents in the N-phenyl ring favor a trans c...

an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

in this paper, we apply the biswas’ idea of anti fuzzy subgroups toideals of near-rings. we introduce the notion of anti fuzzy ideals of near-rings,and investigate some related properties.

equatorial/axial conversion in piperidine and phosphorinane with different substituents wereinvestigated with great details. three possible routes, i.e. heteroatom inversion and two ring inversiontype were considered. ring conversion can occur via two pathways one starts with ring flatteningfrom the heteroatom site (nitrogen in piperidine and phosphorous in phosphorinane) and the otherinitiates...

the effect of alkyl substituents on the c-phenyl and/or the n-phenyl ring of benzophenylhydroxamic acid on their molecular structure and hydrogen bonding has been investigated. the predominant configuration in chcl3 is determined by steric and electronic effects. substituents on the c-phenyl ring favor the cis configuration, while substituents in the n-phenyl ring favor a trans configuration. t...

In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we prove that every element of an abelian neat ring R is twin-good if and only if R has no factor ring isomorphic to‌ Z2  or Z3. The main result of [24] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every elemen...

Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties of $Gamma(R)$ are studied. We investigate connectivity and the girth of $Gamma(R)$, where $...