1-affine completeness of compatible modules

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• 作者：Gary L. Peterson
• 刊名：Algebra Universalis
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：76
• 期：1
• 页码：99-110
• 全文大小：775 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8911
• 卷排序：76

文摘

A faithful compatible module G of a nearring R is 1-affine complete if R equals the set of congruence preserving functions of G that are 0-preserving. The study of 1-affine complete expanded groups G can be approached from this perspective by considering G as a module for the nearring of 0-preserving polynomial functions of G. In this paper, we obtain some strong conditions on the minimal R-ideals of G, when R has dccr and G is 1-affine complete, by using results from papers on units of such nearrings. We then go on to apply these results to obtain necessary and sufficient conditions for G to have a composition series in which each factor of G by a series term is 1-affine complete.Key words and phrasesnearringcompatible moduleexpanded grouppolynomial functioncongruence preserving function1-affine complete