代数和模的J-adic对偶

J-adic dual of algebras and modules

引入了一种Noether代数及其模上的新的对偶,即J-adic对偶,此处,J是给定代数的Jacobson根.证明了Noether代数A的J-adic对偶(记作A□)是余代数,A-模的J-adic对偶是余模;当A是Hopf代数时,若J满足适当的条件,则A的J-adic对偶A□是Hopf代数.

A new method of dual, named J-adic dual, on Noetherian algebras and modules is introduced, where J is the Jacobson radical of a given Noetherian algebra. It is proved that the J-adic dual （denoted by A^□ ） of a Noetherian algebra A is a coalgebra, and the J-adic dual of a module over a Noetherian algebra is a comodule. Moreover, A^□ is a Hopf algebra if A is a Hopf algebra and the Jacobson radical J satisfies some suitable conditions.