论文标题
一类新的在半群和戒指中的广义倒置
A new class of generalized inverses in semigroups and rings with involution
论文作者
论文摘要
让$ s $为$*$ - semigroup，让$ a，w，v \在s $中。这项工作的最初目标是引入两个新类的广义倒置类别，称为$ W $ core倒数，而双$ V $ - 核倒在$ S $中。如果存在一些$ x \，则S $中的元素$ a \是$ w $ core倒置。这样的$ x $称为$ w $ core倒数$ a $。结果表明，可以根据$ w $ core倒数来表征核心逆和伪核逆。衍生出$ w $ core的$ w $ core倒数的几种特征，并且该表达式由$ w $沿$ a $ a $和$ \ {1,3 \} $的倒数给出，$ a $ a $ a $ in $ s $ in $ s $。同样，给出了$ w $ core逆与其他广义逆之间的连接。特别是，当$ s $是$*$ - 戒指时，$ W $ core逆的存在标准由单位给出。 $ a $的双$ v $ - 核由满足$ y^2va = y $，$ y $，$ avay = a $和$（yva）^*= yva $的$ y \的存在来定义。双$ v $ core倒数的双重结果也保持。
Let $S$ be a $*$-semigroup and let $a,w,v\in S$. The initial goal of this work is to introduce two new classes of generalized inverses, called the $w$-core inverse and the dual $v$-core inverse in $S$. An element $a\in S$ is $w$-core invertible if there exists some $x\in S$ such that $awx^2=x$, $xawa=a$ and $(awx)^*=awx$. Such an $x$ is called a $w$-core inverse of $a$. It is shown that the core inverse and the pseudo core inverse can be characterized in terms of the $w$-core inverse. Several characterizations of the $w$-core inverse of $a$ are derived, and the expression is given by the inverse of $w$ along $a$ and $\{1,3\}$-inverses of $a$ in $S$. Also, the connections between the $w$-core inverse and other generalized inverses are given. In particular, when $S$ is a $*$-ring, the existence criterion for the $w$-core inverse is given by units. The dual $v$-core inverse of $a$ is defined by the existence of $y\in S$ satisfying $y^2va=y$, $avay=a$ and $(yva)^*=yva$. Dual results for the dual $v$-core inverse also hold.
