In this paper we investigate a family of algebras endowed with a suitable non-degenerate bilinear form that can be used to define two different notions of dual for a given right ideal. We apply our results to the classification of the right ideals and their duals in the cyclic group algebra, in the Taft algebra and in another example of Hopf algebra arising as bosonization.

中文翻译：

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关于一些代数上的不可分解的理想

在本文中，我们研究了一个代数族，它们具有适当的非退化双线性形式，可用于为给定的理想定义对偶的两个不同概念。我们将结果应用于循环群代数，塔夫脱（Taft）代数和霍普夫（Bopf）代数玻色化的另一个正确理想及其对偶的分类。