On graded characterizations of finite dimensionality for algebraic algebras
Permanent link to this recordhttp://hdl.handle.net/20.500.12613/5675
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Abstract© 2017, Springer International Publishing AG. We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring gr R is right noetherian, if and only if gr R has right Krull dimension, if and only if gr R satisfies a polynomial identity.
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Has partArchiv der Mathematik
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The Problem with Word Problems: An Exploratory Study of Factors Related to Word Problem SuccessByrnes, James P.; Newton, Kristie Jones, 1973-; Ding, Meixia; Booth, Julie L. (Temple University. Libraries, 2016)College Algebra is a gatekeeper course that serves as an obstacle for many students pursuing STEM careers. Lack of success in this course could be a key reason why the United States lags behind other industrialized countries in the number of students graduating with STEM majors and joining the STEM workforce. Of the many topics presented in College Algebra that pose problems, students often have particular difficulty with the application of systems of equations in the form of word problems. The present study aims to identify the factors associated with success and failure on systems of equations word problems. The goal was to identify the factors that remained significant predictors of success in order to build a theory to explain why some students are successful and other have difficulty. Using the Opportunity-Propensity Model of Byrnes and colleagues as the theoretical guide (e.g., Byrnes & Miller-Cotto, 2016), the following questions set the groundwork for the current study: (1) To what extent do antecedent (gender, race/ethnicity, socioeconomic status, and university) and propensity factors (mathematical calculation ability, mathematics anxiety, self-regulation, motivation, and ESL) individually and collectively predict success with systems of equations word problems in College Algebra students, and (2) How do these factors relate to each other? Bivariate correlations and hierarchical multiple regression were used to examine the relationships between the factors and word problem set-up as well as correct completion of the word problems presented. Results indicated after all variables were entered, calculation ability, self-regulation as determined by homework score, and anxiety were the only factors to remain significant predictors of student performance on both levels. All other factors either failed to enter as significant predictors or dropped out when the complete set had been entered. Reasons for this pattern of results are discussed, as are suggestions for future research to confirm and extend these findings.
A direct computation of the cohomology of the braces operadDolgushev, V; Willwacher, T (2017-03-01)© 2017 by De Gruyter. We give a self-contained and purely combinatorial proof of the well-known fact that the cohomology of the braces operad is the operad Ger governing Gerstenhaber algebras.
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