We continue a very fruitful line of inquiry into the multiplicative ideal theory of an arbitrary Leavitt path algebra L. Specifically, we show that factorizations of an ideal in L into irredundant products or intersections of finitely many prime-power ideals are unique, provided that the ideals involved are powers of distinct prime ideals. We also characterize the completely irreducible ideals in L, which turn out to be prime-power ideals of a special type, as well as ideals that can be factored into products or intersections of finitely many completely irreducible ideals.

中文翻译：

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Leavitt 路径代数中素幂理想的乘积和交集

我们继续对任意 Leavitt 路径代数的乘法理想理论进行非常富有成果的研究大号. 具体来说，我们证明了理想的因式分解大号如果所涉及的理想是不同的主要理想的幂，则无限多个素幂理想的冗余乘积或交集是唯一的。我们还刻画了完全不可约的理想大号，结果证明是一种特殊类型的素幂理想，以及可以分解为有限多个完全不可约理想的乘积或交集的理想。