CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt158",{id:"formSmash:upper:j_idt158",widgetVar:"widget_formSmash_upper_j_idt158",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt159_j_idt161",{id:"formSmash:upper:j_idt159:j_idt161",widgetVar:"widget_formSmash_upper_j_idt159_j_idt161",target:"formSmash:upper:j_idt159:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Non-associative Ore extensionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2018 (English)In: Israel Journal of Mathematics, ISSN 0021-2172, E-ISSN 1565-8511, Vol. 224, no 1, p. 263-292Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2018. Vol. 224, no 1, p. 263-292
##### National Category

Mathematics
##### Research subject

ENGINEERING, Mathematics
##### Identifiers

URN: urn:nbn:se:hv:diva-12481DOI: 10.1007/s11856-018-1642-zISI: 000431796000010Scopus ID: 2-s2.0-85044256972OAI: oai:DiVA.org:hv-12481DiVA, id: diva2:1219181
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt465",{id:"formSmash:j_idt465",widgetVar:"widget_formSmash_j_idt465",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt471",{id:"formSmash:j_idt471",widgetVar:"widget_formSmash_j_idt471",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt477",{id:"formSmash:j_idt477",widgetVar:"widget_formSmash_j_idt477",multiple:true});
##### Note

We introduce non-associative Ore extensions, S = R[X; sigma, delta], for any non-ssociative unital ring R and any additive maps sigma, delta : R -> R satisfying sigma(1) = 1 and delta(1) = 0. In the special case when delta is either left or right R-delta-linear, where R-delta = ker(delta), and R is delta-simple, i.e. 0 and R are the only delta-invariant ideals of R, we determine the ideal structure of the non-associative differential polynomial ring D = R[X; id(R),delta]. Namely, in that case, we show that all non-zero ideals of D are generated by monic polynomials in the center Z(D) of D. We also show that Z(D) = R-delta[p] for a monic p is an element of R-delta [X], unique up to addition of elements from Z(R)(delta) . Thereby, we generalize classical results by Amitsur on differential polynomial rings defined by derivations on associative and simple rings. Furthermore, we use the ideal structure of D to show that D is simple if and only if R is delta-simple and Z(D) equals the field R-delta boolean AND Z(R). This provides us with a non-associative generalization of a result by Oinert, Richter and Silve-strov. This result is in turn used to show a non-associative version of a classical result by Jordan concerning simplicity of D in the cases when the characteristic of the field R-delta boolean AND Z(R) is either zero or a prime. We use our findings to show simplicity results for both non-associative versions of Weyl algebras and non-associative differential polynomial rings defined by monoid/group actions on compact Hausdorff spaces.

First Online: 06 March 2018

Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2019-05-28Bibliographically approved
doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1229",{id:"formSmash:j_idt1229",widgetVar:"widget_formSmash_j_idt1229",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1284",{id:"formSmash:lower:j_idt1284",widgetVar:"widget_formSmash_lower_j_idt1284",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1285_j_idt1287",{id:"formSmash:lower:j_idt1285:j_idt1287",widgetVar:"widget_formSmash_lower_j_idt1285_j_idt1287",target:"formSmash:lower:j_idt1285:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});