Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial ring R[{ X, },s/] is a Hilbert ring, where |/| = a. Assume that R is a commutative unitary ring and G is an abelian group. The first research problem listed in [K, Chapter 7] is that of determining equivalent conditions in order that the gr...

In the title mol-ecule, C(12)H(13)N(5)O(2)S, a bifurcated intra-molecular N-H⋯O(O) hydrogen bond forms two S(6) ring motifs. The benzene ring forms a dihedral angle of 14.36 (11)° with the pyrazole ring. In the crystal, pairs of N-H⋯S hydrogen bonds form centrosymmetric dimers, generating R(2) (2)(8) ring motifs, which stack along the b axis.

The complete mol-ecule of the title compound, C(19)H(34)N(2)S, is generated by crystallographic twofold symmetry, with the C=S group lying on the rotation axis. A short C-H⋯S contact occurs in the mol-ecule. The five-membered ring is twisted and the cyclo-hexyl ring adopts a chair conformation. The dihedral angle between the mean plane of the five-membered ring and the basal plane of the cyclo-...

We provide a generalization of pseudo-Frobenius numbers numerical semigroups to the context simplicial affine semigroups. In this way, we characterize Cohen-Macaulay type semigroup ring K[S]. define S, type(S), in terms some Apéry sets S and show that it coincides with ring, when K[S] is Cohen-Macaulay. If d-dimensional embedding dimension at most d+2, then type(S)?2. Otherwise, type(S) might b...

Kodlama teorisinde, lineer kodların özel bir sınıfı olan devirli kodlar ile ilgili araştırmalar büyük ilgi görmektedir. Bu ilginin en önemli nedenlerinden bazıları zengin cebirsel özelliklere sahip olmaları, birçok uygulama alanlarının bulunması, kodlama ve kod çözmede kolaylık sağlamaları olarak sayılabilir. Devirli sabit-devirli, parçalı yarı burmalı kodlargibi genellemeleri bulunmaktadır. ge...

Excited-state properties of aryl carotenoids, important components of light harvesting antennae of green sulfur bacteria, have been studied by femtosecond transient absorption spectroscopy. To explore effects of the conjugated aryl group, we have studied a series of aryl carotenoids with conjugated phi-ring, chlorobactene, beta-isorenieratene and isorenieratene, and compared them with their non...

Hochster established the existence of a commutative noetherian ring R and a universal resolution U of the form 0 ! R ! R ! R ! 0 such that for any commutative noetherian ring S and any resolution V equal to 0! S ! S ! S g ! 0, there exists a unique ring homomorphism R ! S with V = U R S. In the present paper we assume that f = e + g and we nd a resolution of R by free P-modules, where P is a po...

Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ $j\in J\rbrace $ $R\times is called amalgamation along respect to $f$. In this paper, we determine when ^fJ$ (generalized) filter ring.

 In this paper, a new homological dimension of modules, copresented dimension, is defined. We study some basic properties of this homological dimension. Some ring extensions are considered, too. For instance, we prove that if $Sgeq R$ is a finite normalizing extension and $S_R$ is a projective module, then for each right $S$-module $M_S$, the copresented dimension of $M_S$ does not exceed the c...