We show a novel lattice-based scheme (PairTRU) which is a non-commutative variant of the NTRU. The original NTRU is defined via the ring of quotient with variable in integers and this system works in the ring R = Z[x] . We extend this system over Z× Z and it performs all of operations in the non-commutative ring M = M(k,Z×Z)[x] <(Ik×k,Ik×k)x−(Ik×k,Ik×k)> , where M is a matrix ring of k ×...

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 element of a...

Most eukaryotic cells require peroxisomes, organelles housing fatty acid β-oxidation and other critical metabolic reactions. Peroxisomal matrix proteins carry peroxisome-targeting signals that are recognized by one of two receptors, PEX5 or PEX7, in the cytosol. After delivering the matrix proteins to the organelle, these receptors are removed from the peroxisomal membrane or matrix. Receptor r...

Most eukaryotic cells require peroxisomes, organelles housing fatty acid b-oxidation and other critical metabolic reactions. Peroxisomal matrix proteins carry peroxisome-targeting signals that are recognized by one of two receptors, PEX5 or PEX7, in the cytosol. After delivering the matrix proteins to the organelle, these receptors are removed from the peroxisomal membrane or matrix. Receptor r...

We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings‎, ‎then $R/J(R)$ is nil-clean‎. ‎In particular‎, ‎under certain additional circumstances‎, ‎$R$ is also nil-clean‎. ‎These results somewhat improves on achievements due to Diesl in J‎. ‎Algebra (2013) and to Koc{s}an-Wang-Zhou in J‎. ‎Pure Appl‎. ‎Algebra (2016)‎. ‎...

For a field F, let R(n,m) be the ring of invariant polynomials for the action of SL(n,F) × SL(n,F) on tuples of matrices – (A,C) ∈ SL(n,F)× SL(n,F) sends (B1, . . . , Bm) ∈ M(n,F) to (AB1C , . . . , ABmC ). In this paper we call R(n,m) the ring of matrix semi-invariants. Let β(R(n,m)) be the smallest D s.t. matrix semi-invariants of degree ≤ D generate R(n,m). Guided by the Procesi-Razmyslov-Fo...

We present electron microscopic and electron spectroscopic images of putative nucleation sites and early mineral deposits during intramembranous ossification of the murine perichondrial ring. Electron spectroscopic imaging (ESI) permits the quantitative determination and direct visualization of spatial distribution of atomic elements within specimens at high spatial resolution. In this study ES...