论文标题
在适当的$*$ - 戒指中的广义核心逆
Generalized Core Inverse in a proper $*$-ring
论文作者
论文摘要
在本文中，我们在{\ IT $*$ -RING}中介绍了弱核和中央弱核的概念。我们通过产生一些弱核和中心弱核心可逆元素的表示和表征来进一步阐述这两个类别。我们通过其他广义倒置研究了这两类倒置的加性属性和一些显式表达式。此外，还提供了数值示例来验证弱核心倒置的主张。遵循{\ IT $*$ - ring}及其与Clifford代数的互连，我们还介绍了该组反向的示例和弱的核心逆，是不可偶有的不可糊化的quaternion $ \ mathbb {h h} _s $。
In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central weak core invertible elements. We investigated additive properties and a few explicit expressions for these two classes of inverses through other generalized inverses. In addition, numerical examples are provided to validate claims on weak core inverses. Following {\it proper $*$-ring} and their interconnections with Clifford algebra, we also present examples of the group inverse and the weak core inverse of a non-zero non-invertible quaternion $\mathbb{H}_s$.
