a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

Let R be a commutative ring with 1 and M left unitary R-module. In this paper, we give generalization for the notions of compressible (retractable) Modules. We study s-essentially (s-essentially retractable). some their advantages, properties, characterizations examples. also relation between retractable modules) classes modules.

abstract this paper by reviewing the main examples of small to medium-scale retractable roof structures covering building courtyards is to present an innovative rigid retractable roof system employing spatial frames for a courtyard of an existing building in tabriz islamic art university. the courtyard is currently used for temporary exhibitions and gatherings whenever permitted by environmenta...

This is a survey on the usage of the module theoretic notion of a “retractable module" in the study of algebras with actions. We explain how classical results can be interpreted using module theory and end the paper with some open questions.

Abstract This paper by reviewing the main examples of small to medium-scale retractable roof structures covering building courtyards is to present an innovative rigid retractable roof system employing spatial frames for a courtyard of an existing building in Tabriz Islamic Art University. The courtyard is currently used for temporary exhibitions and gatherings whenever permitted by environmenta...

Let be a commutative ring with 1 and left unitary . In this paper, the generalizations for notions of compressible module retractable are given. An is termed to semi-essentially if can embedded in every non-zero semi-essential submodules. module, submodule an Some their advantages characterizations examples We also study relation between these classes some other modules.

A module $M$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $M$ into $M$. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.

human head at 7T. Within one TR we acquire 13 Echoes with a bandwidth of 130 Hz/Px for the TSE part and 930 Hz/Px for the EPI part. The image matrix was 256×182 and the echotime TE=12ms. In a) a regular TSE with 13 echoes is acquired. b) shows a TSE-EPI hybrid with a λLF=0.6. Fig. 1: The k-space simplify scheme of TSE-CAT. The TSE module samples the center part and the EPI module the outer part...

An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M , conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As co...