In this paper we introduce the notion of left ideal, right ideal and ideal in direct-product ring and its applications with examples. We show that-A non-empty subset A X B is an ideal of a direct-product ring G x R if and only if A is a subgroup of G and B is an ideal of R.
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机译：在本文中，我们通过实例介绍左理想，右理想和理想在直接乘积环中的概念及其应用。我们证明-当且仅当A是G的一个子组且B是R的理想时，-一个非空子集A X B是直积环G x R的理想情况。
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