An Ideal Husband, or An Ideal Wife? That is the Question.

Biprojectivty of Banach algebras modulo an ideal

In this paper, we introduce the new concept of biprojectivity of a Banach algebra modulo an ideal, as a generalization of this notion in the classical case. By using it , we obtain some necessary and sufficient conditions for contractibility of Banach algebras modulo an ideal. In particular we characterize the contractibility of quotient Banach algebras. Also we study the relationship between t...

Coherence in amalgamated algebra along an ideal

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

Topics on the Ratliff-Rush Closure of an Ideal

Introduction Let  be a Noetherian ring with unity and    be a regular ideal of , that is,  contains a nonzerodivisor. Let . Then . The :union: of this family, , is an interesting ideal first studied by Ratliff and Rush in [15]. ‎  The Ratliff-Rush closure of  ‎ is defined by‎ . ‎ A regular ideal  for which ‎‎ is called Ratliff-Rush ideal.‎‏‎ ‎ The present paper, reviews some of the known prop...

Is there an ideal behavioural experiment?

M uch of the field of animal behaviour rests on experimental studies of the responses of animals to different classes of stimuli. Playback experiments, which compare responses of animals to tape recordings of different sounds, are a prime example. Consequently, the proper design of these experiments is central to the scientific study of animal behaviour. Over a decade ago, a discussion of the d...

What is an ideal surgical clerkship?