||Group-graded and group-bigraded rings
Hoshino, Mitsuo ,
Kameyama, NoritsuguKoga, Hirotaka
Journal of algebra and its applications
, p.1550100 , 2015-09 , World Scientific
Let I be a nontrivial finite multiplicative group with the unit element e and A = ⨁x∈I Ax an I-graded ring. We construct a Frobenius extension Λ of A and study when the ring extension A of Ae can be a Frobenius extension. Also, formulating the ring structure of Λ, we introduce the notion of I-bigraded rings and show that every I-bigraded ring is isomorphic to the I-bigraded ring Λ constructed above.