幂级数环中的除法理想 $$A+XB[\![X]\!]$$$

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-06-18 DOI:10.1007/s40840-024-01724-1

Hamed Ahmed

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引用次数: 0

摘要

让 $A\subseteq B$ 是一个积分域的扩展，$B[\![X]\!]$ 是关于 B 的幂级数环，并且 $R=A + XB[\![X]\!]$是$B[\![X]\!].$ 在本文中，我们给出了关于 R 的 v-invertible v-ideals （在 A 中的迹不为零）的完整描述。我们证明了，如果 B 是一个完全整闭域，并且 I 是 R 的一个在 A 上有非零迹线的分数可分 v-invertible 理想，那么 $I = u(J_1 + XJ_2[\![X]\!])$ for some $u\in qf(R),$\(J_2/)是B的一个整除v-可逆理想，而（J_1/subseteq J_2/）是A的一个非零理想。

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Divisorial Ideals in the Power Series Ring $$A+XB[\![X]\!]$$

Let $A\subseteq B$ be an extension of integral domains, $B[\![X]\!]$ be the power series ring over B, and $R=A + XB[\![X]\!]$ be a subring of $B[\![X]\!].$ In this paper, we give a complete description of v-invertible v-ideals (with nonzero trace in A) of R. We show that if B is a completely integrally closed domain and I is a fractional divisorial v-invertible ideal of R with nonzero trace over A, then $I = u(J_1 + XJ_2[\![X]\!])$ for some $u\in qf(R),$ $J_2$ an integral divisorial v-invertible ideal of B and $J_1\subseteq J_2$ a nonzero ideal of A.

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来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.