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

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...

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...

A dual-disk ring (DDR) structure with broken symmetry and weakly dissipating material, silver, is proposed to achieve Fano resonance in visible wavelength range. Symmetry breaking of a metallic ring is realized by placing two disks inside the ring. The excitation of the Fano resonance is interpreted in terms of coupling of the ring and the dual-disk plasmonic modes. The potential of using an ar...