【摘要】 总假定 R为含幺有限交换环 ,τ为正整数 .本文证明了 R与其一种有限单扩张同时具有自内射性 ,从而给出“R上任一延迟τ步弱可逆线性有限自动机都有线性延迟τ步弱逆的充要条件是 R为自内射环”的一个新证明 .更多还原

【Abstract】 Let R be a finite commutative ring with identity, τ be a positive integer. We prove in this paper that R and an finite simple extension of R have self-injectivity simultaneously, and based on this,give a new proof for the result that every weakly invertible linear finite automaton over R with delay τ has a linear weak inverse with delay τ if and only if R is a self-injective ring.更多还原