拟Frobenius环的总体维数及其性质

THE GLOBAL DIMENSION AND PROPOSITIONS OF QUASI-FROBENIUS RING

本文讨论了拟Frobenius环(QF环)的总体维数,以及拟Frobenius整环的结构。得出:拟Frobenius环的左、右总体维数或者为∞,或者为零。然后得到:对QF环U,如果U是整环,则U必是主理想整环,最后给出定理:设U为整环,则U是QF环当且仅当U是域。

From this article we can know that the global dimension of quasi-Frobenius ring ol-ny can be ∞ or zero, and we can know that if U is a domain, then U is quasi-Frobenius ring if and only if U is a field.