右理想的级数分解
Serial factorizations of right ideals
摘要：
在Dedekind整环$D$中，每个非零真理想$A$的因子是不同素理想$P_i$的幂的乘积$A=P_1^{t_1}\cdots P_k^{t_k}$。对于Dedekind域$D$，$D$ -模块$D/P_i^{t_i}$是不对称的。我们研究了任意环$R$的右理想$A$的适当分解$A=A_1\dots A_n$作为真右理想$A_1,\dots,A_n$与所有模$R/A_i$ unisolate模的乘积.当这样的因子分解存在时，它们是唯一的，直到因子的阶。序列分解与$h$ -局部Prüfer域和半刚性交换GCD域的理论有联系。
英文摘要：
In a Dedekind domain $D$, every non-zero proper ideal $A$ factors as a product $A=P_1^{t_1}\cdots P_k^{t_k}$ of powers of distinct prime ideals $P_i$. For a Dedekind domain $D$, the $D$-modules $D/P_i^{t_i}$ are uniserial. We extend this property studying suitable factorizations $A=A_1\dots A_n$ of a right ideal $A$ of an arbitrary ring $R$ as a product of proper right ideals $A_1,\dots,A_n$ with all the modules $R/A_i$ uniserial modules. When such factorizations exist, they are unique up to the order of the factors. Serial factorizations turn out to have connections with the theory of $h$-local Prüfer domains and that of semirigid commutative GCD domains.
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