Previous spectroscopic studies on the phycocyanobilin-containing peptide beta-2T from Synechococcus sp. 6301 C-phycocyanin and the phycoerythrobilin-containing peptide beta-2TP from Porphyridium cruentum B-phycoerythrin indicated a different single thioether mode of attachment, postulated to be through the D-ring of the tetrapyrrole, in contrast to the A-ring linkage established for the other s...

If R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field which is algebraic over GF(p), then R has at least one subring S such that S w*=,S,, where each S, is isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings ofR are mutually isomorphic, but not necessarily conjugate in R.

Introduction Let B = k[x 1 ,. .. , x n ] be a polynomial ring over a field k and A = B/J a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[mt] may be considered a standard graded k-algebra and has a presentation B[y 1 ,. In this paper we want to compare the ideals J and I J as well as their homological properties.

Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...

Preliminaries In this lecture, we give a quick review of the basics of classical commutative algebra. The following notation and terminology is used throughout. By a ring we mean a commutative ring with identity. For sets I, J, we write I ⊆ J to denote that I is a subset of J and I ⊂ J to denote that I is a proper subset of J, i.e., I ⊆ J and I = J. We denote the set of nonnegative integers by ...

Let R be a ring with Jacobson radical J and with center C. Let P be the set of potent elements x for which xk = x for some integer k > 1. Let N be the set of nilpotents. A ring R is called subperiodic if R \ (J ∪ C) ⊆ N + P . We consider the commutativity behavior of a subperiodic ring with some constraint involving extended commutators. Mathematics Subject Classification: 16U80, 16D70

Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either E...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

Abstract. Let R be a commutative ring and let n,m be two positive integers. Let AR(n,m) be the polynomial ring in the commuting independent variables xi(j) with i = 1, . . . , m ; j = 1, . . . , n and coefficients in R. The symmetric group on n letters Sn acts on AR(n,m) by means of σ(xi(j)) = xi(σ(j)) for all σ ∈ Sn and i = 1, . . . , m ; j = 1, . . . , n. Let us denote by AR(n,m) Sn the ring ...