半环的半模范畴与加性regular范畴  

Semimodule categories over semirings and additive regular categories

作　　者：任芳[1] 

机构地区：[1]福建船政交通职业学院公共教学部,福建福州350007

出　　处：《福建工程学院学报》2012年第6期529-532,587,共5页Journal of Fujian University of Technology

摘　　要：证明任意半环上的半模范畴是加性regular范畴,并给出半模的函子表示。证明了加性regular范畴关于伴随对的左右平凡扩张范畴是同构的。最后应用至半模范畴,得到半环S的半模范畴S-SMod关于Hom函子HomS(M,)的左平凡扩张范畴HomS(M,)∝S-SMod和S-SMod关于张量函子MS-的右平凡扩张范畴S-SMod∝S-是范畴等价。The category of semimodules over a semiring is shown to be an additive regular category, and then the functorial representation of a module is given. Moreover, the left and right trivial exten- sions of an additive regular category are proved to be isomorphic under the adjoint situation. Finally, the result is applied to the semimodule category, which gives rise to the isomorphism of Homs （M,） ∝S- SMod with the left trivial extension of S- SMod by Horn functor Homs（M, ） and S- SMod M×s- the right trivial extension of S - SMod by tensor functor M×s-.

关 键 词：半环 半模 regular范畴 平凡扩张 

分 类 号：O154.1[理学—数学]