The main goal of this paper is to give a mathematical foundation, serious and consistent, to some parts of Santillis isotheory. We study the isotopic liftings of rings, subrings and ideals, and we also introduce the concept of quotient isoring. By using the isoproduct model, necessary conditions assuring the existence of such isostructures are given. Such conditions are based on the inner laws which originate the associated elements of isotopy. These elements will allow to extend, from a different point of view, the Santillis study of non-linear generalized theory. Several examples of these isostructures are also shown. We finally find the differences between a quotient isoring and a quotient ring coming from an isoring and one of its isoideals.
Lo scopo principale di questo articolo è dare una fondazione matematica, seria e costante a delle parti dell'isoteoria di Santilli. Noi studiamo i sollevamenti isotopici di anelli, sottoanelli ed ideali. Usando il modello della isomoltiplicazione, condizioni necessarie che assicurano l'esistenza di tali isostrutture sono date. Tali condizioni sono basate sulle leggi interne che originano gli elementi associati di sollevamenti isotopici. Questi elementi permetteranno di estendere, da un punto di vista diverso lo studio di Santilli di teoria generalizzata e non-lineare. Molti esempi di queste isostrutture sono dati. Noi troviamo infine le differenze tra un isoanello quoziente ed un anello quoziente provenienti da un isoanello e da uno dei suoi isoideali.
@article{BUMI_2005_8_8B_2_437_0,
author = {Ra\'ul M. Falc\'on and Juan N\'u\~nez Vald\'es},
title = {Isorings and related isostructures},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {8-A},
year = {2005},
pages = {437-452},
zbl = {1137.16305},
mrnumber = {2149395},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_2_437_0}
}
Falcón, Raúl M.; Núñez Valdés, Juan. Isorings and related isostructures. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 437-452. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_2_437_0/
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