论文标题
i-可逆环的扩展
Extensions of I-Reversible Rings
论文作者
论文摘要
如果对于每个$ a，b $ \ in $ $ r $，$ ab $，$ r $ $ r $，$ ab $是一个非零的iDempotent，则意味着$ ba $是iDempotent。众所周知，环$ m_n（r）$和$ t_n（r）$（$ r $ $ r $上的所有上三角矩阵的环）对于$ n \ geq 3 $不可逆转。在本文中，当$ n \ geq 3 $和$ r $只有$ m_n（r）$的非平凡的i-可逆supring，而$ r $仅具有微不足道的diadempotents。如果$ r $是一个字段，我们还为每个$ n \ geq 3 $提供了$ t_n（r）$的最大i-可逆suzring。然后，我们提供了琐碎，多罗（Dorroh）和长田（Nagata）扩展的可逆性条件。最后，我们提供了一些独立的条件，以实现多项式环的可逆性，更普遍地是偏斜多项式环。
A ring $R$ is said to be i-reversible if for every $a,b$ $\in$ $R$, $ab$ is a non-zero idempotent implies $ba$ is an idempotent. It is known that the rings $M_n(R)$ and $T_n(R)$ (the ring of all upper triangular matrices over $R$) are not i-reversible for $n \geq 3$. In this article, we provide a non-trivial i-reversible subring of $M_n(R)$ when $n \geq 3$ and $R$ has only trivial idempotents. We further provide a maximal i-reversible subring of $T_n(R)$ for each $n\geq 3$, if $R$ is a field. We then give conditions for i-reversibility of Trivial, Dorroh and Nagata extensions. Finally, we give some independent sufficient conditions for i-reversibility of polynomial rings, and more generally, of skew polynomial rings.
