科研之友
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摘要
Let R be a ring with unity 1. We introduce the definition of the (dual) polarity along an element in R. Given any a, d & ISIN; R, an element a is polar along d if there exists some p & ISIN; R such that p2 = p & ISIN; comm(da), pd = d and da +1 - p is a unit. Also, the dual polarity along an element is given. Simply polar elements, polar elements and well-supported elements are special cases of polar elements along d. Moreover, several properties and characterizations of the polarity along an element are investigated.
