Let us fix the usual notation • C is a geometrically connected smooth projective curve over a finite field Fq. • ∞ ∈ C is a closed point. • F = Fq(C) is the function field of C. • A = H(C − {∞},OC) is the ring of functions on C that are regular outside ∞. • Â = lim0 6=I⊂AA/I and Af = Â⊗A F . • F∞ is the completion of F at ∞ with valuation ring O∞. The ring A is discrete inside F∞, and the absol...

Diberikan sebarang ring R dan semigrup S. Ring R[S] adalah himpunan semua fungsi f dari S ke dengan supp(f) berhingga yang dilengkapi operasi penjumlahan pergandaan sama pada polinomial R[X]. Di sisi lain, matriks M_n (R) atas berukuran n×n perkalian matriks. dalam penelitian ini, dikonstruksi (R_1 [S_1 ] ) (R_2 [S_2 R_1,R_2 S,S_2 semigrup. Selain itu, didefinisikan pemetaan τ menggunakan homom...

Let F = {Fn} be a multiplicative filtration of a local ring such that the Rees algebra R(F) is Noetherian. We recall Burch’s inequality for F and give an upper bound of the a-invariant of the associated graded ring a(G(F)) using a reduction system of F . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension 2.

Many practical lattice-based schemes are built upon the Ring-SIS or Ring-LWE problems, which are problems that are based on the presumed difficulty of finding low-weight solutions to linear equations over polynomial rings Zq[x]/〈f〉. Our belief in the asymptotic computational hardness of these problems rests in part on the fact that there are reduction showing that solving them is as hard as fin...

Let q be an odd prime power, and denote by $${\mathbb {F}}_q$$ the finite field with elements. In this paper, we consider ring $$R={\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb , where $$u^2=u, v^2=v,uv=vu=0$$ study double circulant negacirculant codes over ring. We first obtain necessary sufficient conditions for a code to self-dual (resp. LCD). Then enumerate LCD R. Last but not least, show that...

let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such tha...

A group of 1,3-biarylhydrazide derivatives possessing a COX-2 azido pharmacophore at the Para- position of the C-1 phenyl ring in conjunction with a N-3 phenyl or substituted-phenyl ring (4-F,4-Cl,4-OMe) were designed and synthesized based on nucleophilic substitution reaction. A molecular modelling study of these compounds showed that the designed molecules were well bound with the active site...

Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...