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In mathematics, Lazard's universal ring is a ring introduced by Michel Lazard in over which the universal commutative one-dimensional formal group law is defined. There is a universal commutative one-dimensional formal group law over a universal commutative ring defined as follows. We let :''F''(''x'', ''y'') be :''x'' + ''y'' + Σ''c''''i'',''j'' ''x''''i''''y''''j'' for indeterminates :''c''''i'',''j'', and we define the universal ring ''R'' to be the commutative ring generated by the elements ''c''''i'',''j'', with the relations that are forced by the associativity and commutativity laws for formal group laws. More or less by definition, the ring ''R'' has the following universal property: :For every commutative ring ''S'', one-dimensional formal group laws over ''S'' correspond to ring homomorphisms from ''R'' to ''S''. The commutative ring ''R'' constructed above is known as Lazard's universal ring. At first sight it seems to be incredibly complicated: the relations between its generators are very messy. However Lazard proved that it has a very simple structure: it is just a polynomial ring (over the integers) on generators of degrees 2, 4, 6, … (where ''c''''i'',''j'' has degree 2(''i'' + ''j'' − 1)). proved that the coefficient ring of complex cobordism is naturally isomorphic as a graded ring to Lazard's universal ring. ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lazard's universal ring」の詳細全文を読む スポンサード リンク
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