MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS

Contracting Endomorphisms and Gorenstein Modules

A finite module M over a noetherian local ring R is said to be Gorenstein if Ext(k, M) = 0 for all i 6= dimR. A endomorphism φ : R → R of rings is called contracting if φ(m) ⊆ m for some i ≥ 1. Letting R denote the R-module R with action induced by φ, we prove: A finite R-module M is Gorenstein if and only if HomR( R,M) ∼= M and ExtiR( R,M) = 0 for 1 ≤ i ≤ depthR.

Real Hypersurfaces of a Complex Projective Space Satisfying Certain Conditions

The objective of the present paper is to study real hyper surfaces of a complex projective space with generalized recurrent second fundamental tensor and it is shown that such type real hyper surface exist. Also, we study real hyper surfaces of a complex projective space with generalized recurrent Ricci tensor. It is proved that a real hyper surfaces of complex projective space is generalized R...

Certain Subclasses of Bi–univalent Functions Satisfying Subordinate Conditions

In this paper, we introduce and investigate each of the following subclasses: SΣ(λ ,γ ;φ), H S Σ(α), RΣ(η ,γ ;φ) and BΣ(μ ;φ) (0 λ 1; γ ∈ C {0}; α ∈ C; 0 η < 1; μ 0) of bi-univalent functions, φ is an analytic function with positive real part in the unit disk D, satisfying φ(0) = 1, φ ′(0) > 0, and φ(D) is symmetric with respect to the real axis. We obtain coefficient bounds involving the Taylo...

Sperner families satisfying additional conditions and their convex hulls

The profile of a hypergraph on n vertices is (f0 ..... fn) where fi denotes the number of /-element edges. The extreme points of the set of the profiles are determined for Sperner hyper-graphs satisfying some additional conditions. The results contain some old theorems of extremal set theory as particular cases.

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra