发表机构
CR4AI（CR4AI）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究正式矩阵环的对合性质，通过Morita上下文构造并描述三角环中的对合，证明若所有对角环具此性质则任意有限阶正式矩阵环也具此性质，并给出例证。
AI 中文摘要
我们研究了具有对合性质的正式矩阵环，即环中每个元素都可以表示为一个可逆元素与一个对合之和。在回顾了通过Morita上下文构造正式矩阵环之后，我们描述了三角正式矩阵环中的对合，并建立了二阶上三角环的判定准则。随后，我们证明了任意有限阶的正式矩阵环，当其所有对角环都具有该性质时，该环也具有对合性质。文中包含若干例子和反例以说明所得结果。
英文摘要
We study formal matrix rings with the involution property, that is, rings in which every element can be represented as the sum of an invertible element and an involution. After recalling the construction of formal matrix rings via Morita contexts, we describe involutions in triangular formal matrix rings and establish a criterion for upper triangular rings of order two. We then prove that a formal matrix ring of arbitrary finite order has the involution property whenever all of its diagonal rings have this property. Several examples and counterexamples are included to illustrate the obtained results.
