科研之友
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摘要
In this paper, we introduce the tuition or an action Y(X) as a generalization of the notion module. and the notion of it norm Delta: Y(X) -> F. where F is a field and Delta (xy) Delta (y') = Delta (y) Delta (xy') as well as the notion of fuzzy norm, where Delta: YX -> [0, 1] subset of R, with R the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that Ker Delta = {y vertical bar Delta (y) = 0} has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements' of subactions N(X) of Y(X).
- 出版日期2010-6
