in this work, we investigate the transfer of some homological properties from a ring $r$ to its amalgamated duplication along some ideal $i$ of $r$ $rbowtie i$, and then generate new and original families of rings with these properties.

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the de nitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

In an earlier paper we established that every second countable, completely normal spectral space is homeomorphic to the ℓ-spectrum of some Abelian ℓ-group. We extend result ℓ-spectra vector lattices over any countable totally ordered division ring k. Combining those methods with Baro's Normal Triangulation Theorem, obtain following result: TheoremFor formally real field k, spectrum commutative ...

three siblings (1 boy, 2 girls) with hypertension and hypokalemia are presented, two with low plasma aldosterone and suppressed renin activity and the eldest with a high renin and aldosterone level due to secondary changes in her kidneys. urinary tetrahydrocortisol (thf) was increased relative to tetrahydrocortisone (the). cortisol ring a reduction constant was also lower than normal. these fin...

The main objects of this paper are the graded automorphisms of w x polytopal semigroup rings, i.e., semigroup rings k S where k is a field P Ž and S is the semigroup associated with a lattice polytope P Bruns, P w x. w x Gubeladze, and Trung BGT . The generators of k S correspond bijecP tively to the lattice points in P, and their relations are the binomials representing the affine dependencies...

Much is known about the Freedericksz transition induced by uniform electric and magnetic fields in nematic liquid crystals. In this work, we are interested effects of a spatially varying field on transition. Specifically, study director configuration homeotropic cell with cylindrical symmetry. The experiment conducted ring magnet which provides radial magnitude monotonically decreasing to zero ...