An holomorphic study of the Smarandache concept in loops. From: Scientia Magna | Date: January 1, 2006| Author: | COPYRIGHT 2006 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.  All inquiries regarding rights should be directed to the Gale Group.Copyright information

Abstract If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop. This statement is also shown to be true for some weak Smarandache loops (inverse property, weak inverse property) but false for others (conjugacy closed, Bol, central, extra, Burn, A-, homogeneous) except if their holomorphs are nuclear or central. A necessary and sufficient condition for the ...

Related newspaper, magazine, and trade journal articles from HighBeam Research

(Including press releases, facts, information, and biographies)

	An holomorphic study of Smarandache automorphic and cross inverse property loops.(Report) ; ...automorphic inverse property quasigroups...and cross inverse property quasigroups...automorphic inverse property loop (AIPL), cross inverse property loop(CIPL...quasigroup) is a weak inverse property loop (quasigroup...is a cross inverse ...
	On the universality of some Smarandache loops of Bol-Moufang type. ; ...Smarandache left(right) inverse property loop in which...a Smarandache inverse property loop in which...Smarandache: left(right) inverse property loops and inverse property loops. Keywords...Smarandache : inverse property loops (IPL), weak inverse ...
	Electrically conductive adhesives get smaller.(Epoxy adhesives) ; ...cure at room temperature given enough time. The conductivity of a material is typically reported as a readily measured inverse property, resistivity. Choice of Conductive Materials A variety of conductive elements are available to the compounder. Carbon black...
	Understanding the significance of context: a framework to examine equity and reform in secondary mathematics. ; ...what opposite means. A student says that it means to change the sign. The teacher tells the students to write additive inverse property in their notes. She then instructs the students to write -3/4 in their notes and to find the opposite. A student says that...
	Modern school mathematics.(Essay) ; ...the associative property of addition and multiplication * the distributive property of multiplication over addition * the inverse property of subtraction and division * the property of closure. Set theory and venn diagrams received much emphasis, also, as did...
	REFRACTORY FALLACIES.(common myths)(Brief Article) ; ...the detrimental effects of cool/cold temperatures are avoided. Many important topics like raw materials, microstructure, inverse property relationships, quality control, shelf life and others could also have been mentioned here. Suffice it to say that proper...

For more facts and information, see all results