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ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCarlons. Organic oligomers from condensation of carbon dinucleophiles with difunctional derivatives of carboxylic acidsLawrence B. Kool and George M. WhitesidesCite this: J. Am. Chem. Soc. 1988, 110, 1, 306–307Publication Date (Print):January 1, 1988Publication History Published online1 May 2002Published inissue 1 January 1988https://pubs.acs.org/doi/10.1021/ja00209a058https://doi.org/10.1021/ja00209a058research-articleACS PublicationsRequest reuse permissionsArticle Views98Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts
When a region of intense shear in a slope is much thinner than other relevant geometric lengths, this shear failure may be approximated as localized slip, as in faulting, with strength determined by frictional properties of the sediment and effective stress normal to...
Throughout this paper («, M, N, S) will denote a Morita context satisfying a certain nonsingularity condition.For such contexts we give necessary and sufficient conditions in terms of M and « for S to have a semisimple maximal left quotient ring; respectively a full linear maximal left quotient ring, a semisimple classical left quotient ring.In doing so we extend the corresponding well-known theorems for rings (employing them in the process) to endomorphism rings. Suppose (R, M, N, S) is a Morita context ([1], [2]).That is suppose RMS and SNR are bimodules with an R-R bimodule homomorphism ( , ) : M ®s N^R and an S-S bimodule homomorphism [, ] : N ®R M->S satisfying mAjty, m2] = (/»!, nf)m2 and nY(mx, n2) = [nlt mx]n2 for all mlt m2e N and n,, n2 e N.Throughout, unless otherwise indicated, M and JV will satisfy the following condition: Ms is faithful; and [N,m]=0 for me M implies that m=0.Note that when this condition is satisfied, we can (and will) assume that SçHomR(M, M).Let RM be any left /(-module, and set N=HomR(M, R) and 5= Homñ(M, M).Set (m,f) = (m)f for m e M,fe N; and [/, m] is defined via mx[f, m] = (m1,f)m for all m, w, e M,feN.Then (R, M, N, S) is a Morita context, called the standard context for RM.If R is semiprime and RM is torsionless, then the above condition is satisfied by the standard Morita context for RM.If RM is a generator and 1 e R; or indeed, if (Trace RM)m^0 whenever O^m e M, then the standard Morita context for RM satisfies the above condition.Lemma 1.(a) If A is an essential left ideal ofS, then MA is an essential submodule of RM.