泛Osborn环中的新恒等式
New Identities In Universal Osborn Loops
摘要：
2005年，Michael Kinyon提出了一个开放性问题（Is Every Osborn loop universal？得到了回答。建立了刻画泛Osborn环（左泛Osborn环和右泛Osborn环）的两个恒等式.许多新的身份建立普遍（左和右普遍）奥斯本循环，如CC-循环，VD-循环和普遍弱逆性质循环。特别地，令人惊讶地发现Moufang环服从新恒等式$[y(x^{-1}u)\cdot u^{-1}](xu)=[y(xu)\cdot u^{-1}](x^{-1}u)$.首次在泛Osborn环（左泛和右泛）中引入并研究了新的环性质，它们是已知环性质如逆性质、幂结合性和非结合性的较弱形式.其中一些条件是泛Osborn是3次结合的充要条件。例如，其中四个是CC环是幂结合的新的充要条件。一个共轭闭回路被证明是双结合的当且仅当它是幂结合的，并具有弱形式的双结合性。
英文摘要：
A question associated with the 2005 open problem of Michael Kinyon (Is every Osborn loop universal?), is answered. Two nice identities that characterize universal (left and right universal) Osborn loops are established. Numerous new identities are established for universal (left and right universal) Osborn loops like CC-loops, VD-loops and universal weak inverse property loops. Particularly, Moufang loops are discovered to obey the new identity $[y(x^{-1}u)\cdot u^{-1}](xu)=[y(xu)\cdot u^{-1}](x^{-1}u)$ surprisingly. For the first time, new loop properties that are weaker forms of well known loop properties like inverse property, power associativity and diassociativity are introduced and studied in universal (left and right universal) Osborn loops. Some of them are found to be necessary and sufficient conditions for a universal Osborn to be 3 power associative. For instance, four of them are found to be new necessary and sufficient conditions for a CC-loop to be power associative. A conjugacy closed loop is shown to be diassociative if and only if it is power associative and has a weak form of diassociativity.
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