The main goal of this paper is to extend Flanigan’s theorem in [4] concerning ideal essential extensions of rings to left ideal essential extensions. Moreover, we give new proofs of two Flanigan’s theorems and answer a question raised by M. Petrich in [5] which is related to pure extensions of rings.

中文翻译：

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左上环的理想基本延伸

本文的主要目标是将 [4] 中关于环的理想本质扩展的 Flanigan 定理扩展到左理想本质扩展。此外，我们给出了两个 Flanigan 定理的新证明，并回答了 M. Petrich 在 [5] 中提出的与环的纯扩展有关的问题。