Let [Formula: see text] be a commutative ring with text]. We introduce the concept of weakly 1-absorbing primary ideal, which is generalization ideal. A proper ideal said to if whenever nonunit elements and text], we have or number results concerning ideals are given, as well examples ideals. Furthermore, give corrected version result on rings.

Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly rings and invertible discuss the relations between these several properties of rings. Also, study concept crossed products some defined product give relationship Moreover, in generalization for essential submodules, semi-uniform modules which is uniform modules.

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 ...

We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits...

In the title compound, C(11)H(16)ClNO, the side chain of the ethyl-amine group is almost perpendicular to the benzene ring; the dihedral angle between the C/C/N plane of the ethyl-amine grouping and the benzene plane is 87.4 (2)°. An intramolecular N-H⋯O hydrogen bond occurs. In the crystal structure, mol-ecules are connected weakly by O-H⋯N hydrogen bonds, forming a tetra-mer around the symmet...

Bott periodicity for the unitary and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with …nite coe¢ cients, similar results are consequences of the Milnor and Bloch-Kato conjectures, a¢ rmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodici...

We investigate the relationship between level of a bounded complex over commutative ring with respect to class Gorenstein projective modules and other invariants or ring, such as dimension, Krull dimension. The results build upon work done by J. D. Christensen [7], H. Altmann et al. [1], Avramov [4] for levels finitely generated modules.

We analyze polynomials Pn that are biorthogonal to exponentials {e−σn,j }j=1, in the sense that ∫ ∞ 0 Pn(x)e −σn,j x dx = 0, 1 ≤ j ≤ n. Here α >−1. We show that the zero distribution of Pn as n→∞ is closely related to that of the associated exponent polynomial Qn(y)= n ∏ j=1 (y + 1/σn,j )= n ∑ j=0 qn,j y j . More precisely, we show that the zero counting measures of {Pn(−4nx)}∞n=1 converge weak...

We identify several orbital resonances involving the newly discovered satellites, 1986U7 and 1986U8, and the Uranian rings. The most important resonances in eccentric rings are known as eccentric resonances and are generalizations of the more familiar Lindblad resonances. In keeping with the notation established for Lindblad resonances, we distinguish inner and outer eccentric resonances by the...