Fine rings: A new class of simple rings

Calugareanu G.; Lam T. Y.

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Fine rings: A new class of simple rings

机译：细戒指：一类新的简单戒指

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A nonzero ring is said to be fine if every nonzero element in it is a sum of a unit and a nilpotent element. We show that fine rings form a proper class of simple rings, and they include properly the class of all simple artinian rings. One of the main results in this paper is that matrix rings over fine rings are always fine rings. This implies, in particular, that any nonzero (square) matrix over a division ring is the sum of an invertible matrix and a nilpotent matrix.

机译：如果非零环中的每个非零元素都是一个单位和一个幂元素的和，则称非零环是好的。我们显示出细环构成了简单环的适当类别，并且它们适当地包括了所有简单阿蒂尼亚环的类别。本文的主要结果之一是细环上的矩阵环始终是细环。这特别意味着，除法环上的任何非零（正方形）矩阵都是可逆矩阵和幂等矩阵的和。

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《Journal of algebra and its applications》 |2016年第9期|共18页
作者
Calugareanu G.; Lam T. Y.;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Units; nilpotents; matrix rings; artinian rings; simple rings; clean rings; fine rings; UU rings;

机译：单位;幂零;矩阵环;阿丁环;简单环;清洁环;细环;UU环;

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1. Fine rings: A new class of simple rings [J] . Calugareanu G., Lam T. Y. Journal of algebra and its applications . 2016,第9期

机译：细戒指：一类新的简单戒指
2. A finer classification of the unit sum number of the ring of integers of quadratic fields and complex cubic fields [J] . Nahid Ashrafi Proceedings Mathematical Sciences . 2009,第3期

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3. A finer classification of the unit sum number of the ring of integers of quadratic fields and complex cubic fields [J] . NAHID ASHRAFI Proceedings of the Indian Academy of Sciences . 2009,第3期

机译：二次场和复三次场的整数环的单位和数的更精细分类
4. Sufficient Conditions for a Dubrovin Valuation Ring of a Simple Artinian Ring to be Nil-clean [C] . Muhamad Faikar Mustafidz Al Habibi, Santi Irawati, Hery Susanto, International Conference on Mathmatics and Its Applications . 2019

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7. Rings whose class of projective modules is socle fine [O] . Idelhadj Abdelouahab 2004

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Fine rings: A new class of simple rings

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