Special Radical Research Articles

RADICAL PSYCHOLOGY

Medical Journal of AustraliaVolume 2, Issue 21 p. 789-790 Special Review RADICAL PSYCHOLOGY Murray McLachlan, Murray McLachlanSearch for more papers by this author Murray McLachlan, Murray McLachlanSearch for more papers by this author First published: 01 November 1974 https://doi.org/10.5694/j.1326-5377.1974.tb71174.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume2, Issue21November 1974Pages 789-790 RelatedInformation

WEAKLY SPECIAL AND SPECIAL RADICALS IN SEMIGROUPS

Hoehnke radicals on the class of semigroups are considered. The concepts of the special and weakly special radical in semigroups are introduced; they are analogous to the ring concepts. A characterization of reductive semigroups as those which possess a universal property for extensions is found. It is proved that the least special and least weakly special radicals coincide. A connection between the least special radical and the lower radical of Hoehnke is revealed. Bibliography: 15 items.

A Construction in General Radical Theory

Given an arbitrary associative ring R we consider the ring R[x] of polynomials over R in the commutative indeterminate x. For each radical property S we define the function S* which assigns to each ring R the idealof R. It is shown that the property SA (that a ring R be equal to S*(R)) is a radical property. If S is semiprime, then SA is semiprime also. If S is a special radical, then SA is a special radical. SA is always contained in S. A necessary and sufficient condition that S and SA coincide is given.The results are generalized in the last section to include extensions of R other than R[x], One such extension is the semigroup ring R[A], where A is a semigroup with an identity adjoined.