We develop the theory of “branch algebras”, which are infinitedimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which • is finitely generated and infinite-dimensional, but has only finite-dimensional qu...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in commutative rings. Let \(G\) be a group \(R\) \(G\)-graded ring with nonzero identity \(1\neq0\). A proper ideal \(P\) of is called if for each nonunits \(x,y,z\in h(R)\) \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties characterizations ideals. Moreover, investigate under homomorph...

In the title mol-ecule, C22H12N6, the fused tetracyclic core shows a small lengthwise twist as indicated by the dihedral of 2.7 (2)° between the outer rings. In the crystal, mol-ecules stack along the b-axis direction via offset π-stacking [centroid-centroid distances = 3.5282 (13) and 3.5597 (14) Å] with the stacks weakly associated through C-H⋯N hydrogen bonds. The phenyl ring is rotationally...

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $$A $$ be a ring with nonzero identity $$1\ne 0.$$ A proper ideal $$P of is said to if for every nonunits $$x,y,z\in $$0\ne xyz\in P, then $$xy\in P$$ or $$z\in P. In addition give many properties characterizations ideals, we also determine rings which prime. Furthermore, investigate C(X), the continuous...

In the mononuclear title complex, [Co(N3)2(C12H8N4S)2], the cobalt(II) atom is located on an inversion centre and displays an axially weakly compressed octa-hedral coordination geometry. The equatorial positions are occupied by the N atoms of two 2,5-bis-(pyridin-2-yl)-1,3,4-thia-diazole ligands, whereas the axial positions are occupied by N atoms of the azide anions. The thia-diazole and pyrid...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

Viscous overstability (oscillatory instability) may play an important role in the formation of small scale structure in dense planetary rings such as Saturn's B ring. We investigate the growth and saturation of such modes in local particle simulations. Starting from a hydrodynamic model, we develop a set of ordinary differential equations to model the evolution of the amplitudes of the linearly...

We introduce the notion of Burch submodules and weakly m-full modules over a local ring (R,m) study their properties. One our main results shows that satisfy 2-Tor rigid test also show (R,m), submodule M finitely generated R-module X, such either M=mX or M(⊆mX) is in 1-Tor rigid, module provided X faithful (and X∕M has finite length when m-full). As an application, we give some new class rings ...