An automaton A is called a retractable automaton if, for every subau-tomaton B of A, there is at least one homomorphism of A onto B which leaves the elements of B fixed (such homomorphism is called a retract ho-momorphism of A onto B). We say that a retractable automaton A=(A,X,δ) is Boolean-type if there exists a family {λ B | B is a subautomaton of A} of retract homomorphisms λ B of A such th...

A homomorphism of an automaton A without outputs onto a subau-tomaton B of A is called a retract homomorphism if it leaves the elements of B fixed. An automaton A is called a retractable automaton if, for every subautomaton B of A, there is a retract homomorphism of A onto B. In [1] and [3], special retractable automata are examined. The purpose of this paper is to give a construction for state...

Building on Hrushovski’s work in [5], we study definable groupoids in stable theories and their relationship with 3-uniqueness and finite internal covers. We introduce the notion of retractability of a definable groupoid (which is slightly stronger than Hrushovski’s notion of eliminability), give some criteria for when groupoids are retractable, and show how retractability relates to both 3-uni...

a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

We call a module  essentially retractable if HomR for all essential submodules N of M. For a right FBN ring R, it is shown that: (i)  A non-zero module  is retractable (in the sense that HomR for all non-zero ) if and only if certain factor modules of M are essentially retractable nonsingular modules over R modulo their annihilators. (ii)  A non-zero module  is essentially retractable if and on...

A new versatile transbronchial needle, the modified type 2B retractable needle, was used for the staging and diagnosis of bronchogenic carcinoma. It combines the advantages of its predecessors, the fixed type 1A needle and the retractable type 2A needle, such as convenience of usage and the added ability to sample peripheral as well as central lesions. The new modified type 2B retractable needl...

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.