イデアル化によって得られたArtin Gorenstein局所環内のgood idealsの構造と分布について

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概要

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• Let I be an m-primary ideal in a Gorenstein local ring A with the maximal ideal m and d=dim A Assume that I contains a parameter ideal Q in A as a reduction. Then we say that / is a good ideal in A, if [numerical formula] is a Gorenstein ring and a(G)=1-d. In [GIW] a theory of good ideals is developed. In the present paper we are interested in the special case where d=0. If d=0, I is a good ideal in A if and only if I^2=(0) and 2l_A(I)=l_A(A), where l_A (*) denotes the length. Firstly we determine the structure of good ideals in A in terms of ideals α in R with α^2=(0) and certain special homomorphisms [numerical formula] in the case where [numerical formula] is the trivial extension of an Artinian local ring (R,n) by the injective hull E=E_R(R/n) of the residue field R/n. Secondly we explore a few examples to illustrate the theorem.

• 明治大学の論文

著者

• 後藤 四郎

  Department of Mathematics School of Science and Technology, Meiji University

• 原井川 聡

  Department of Mathematics School of Science and Technology, Meiji University

• 原井川 聡

  Department Of Mathematics School Of Science And Technology Meiji University

関連論文

• 有限群のRees代数への作用とその不変部分環のGorenstein性について(II)
• 随伴次数環の正準加群への埋め込み
• 有限群のRees代数への作用とその不変部分環のGorenstein性について
• イデアル化によって得られたArtin Gorenstein局所環内のgood idealsの構造と分布について

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