1 In this paper we consider reduced homogeneous ideals J ⊂ S of a polynomial ring S, having a 2-linear resolution. 1. We study systems of generators of J ⊂ S. 2. We compute the arithmetical rank for a large class of projective curves having a 2-linear resolution. 3. We show that the fiber cone projF(IL) of a lattice ideal IL of codimension two is a set theoretical complete intersection.

LetR be a commutative ring and let n,m be two positive integers. Let AR(n,m) := R[x11, . . . , x1m, . . . , xn1, . . . , xnm] be the polynomial ring in the commuting independent variables x11, . . . , x1m, . . . , xn1, . . . , xnm with coefficients in R. The symmetric group on n letters Sn acts on AR(n,m) by means of σ(xij) = xσ(i) j for all σ ∈ Sn and i = 1, . . . , n ; j = 1, . . . , m. Let u...

Let $(R,\mathfrak m)$ be a Noetherian local ring of prime characteristic p > 0, and t an integer such that $H_{\mathfrak m}^{j}(R)/0^{F}_{H^{j}_{\mathfrak m}(R)}$ has finite length for all j < t. The aim this paper is to show there exists uniform bound Frobenius test exponents ideals generated by filter regular sequences at most

We give a criterion for when idempotents of a ring R which commute modulo the Jacobson radical J(R) can be lifted to commuting idempotents of R. If such lifting is possible, we give extra information about the lifts. A “half-commuting” analogue is also proven, and this is used to give sufficient conditions for a ring to have the internal exchange property. In particular, we show that if R/J(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)‎. ‎...

The physical urticarias are a heterogeneous subgroup of chronic urticarias in which wheals can be reproducibly induced by different specific physical stimuli such as cold, heat, pressure, vibration, or sunlight. Physical urticarias comprise up to 25 % of chronic urticarias and occur more frequently in young adults. Symptoms, i.e. wheal and flare responses or angioedema, are usually limited to t...

We address an error in the original paper [1]. Proposition 3.1 in [1] was incorrect as stated. In particular, the purported implications 2 =⇒ 1 and 3 =⇒ 1 are false; there exists a real closed field R, a Z-ring I ⊂ R, and a ∈ R − I such that p(a) is infinite or in Z for all p(x) ∈ I[x], but there is no Z-ring J such that I ⊂ J ⊂ R and a ∈ J . We thank Emil Jeřábek [2] for pointing out the error...

In this paper we derive a Gilbert-Varshamov type bound for linear codes over Galois rings. For linear codes over the Galois ring GR(pl; j) the result can be stated as follows. Given r; such that 0 < r < 1 and 0 < H 1 pj (1 r): Then for all n N; where N is a sufficiently large integer, there exist [n; k] GR linear codes over GR(pl; j) such that k=n r and d=n : Consequently, this bound does not g...

The N-terminus of full-length RAG1, though dispensable for RAG1/2 cleavage activity, is required for efficient V(D)J recombination. This region supports RING E3 ubiquitin ligase activity in vitro, but whether full-length RAG1 functions as a single subunit or a multi-subunit E3 ligase in vivo is unclear. We show the multi-subunit cullin RING E3 ligase complex VprBP/DDB1/Cul4A/Roc1 associates wit...