[PDF][PDF] Strongly graded rings which are maximal orders
Sci. Math. Jpn, 2019•jams.jp
Let R=⊕ n∈ ZRn be a strongly graded ring of type Z. In [6], it is shown that if R0 is a
maximal order, then so is R. We define a concept of Z-invariant maximal order and show R0
is a Z-invariant maximal order if and only if R is a maximal order. We provide examples of R0
which are Z-invariant maximal orders but not maximal orders. 1 Introduction Let R=⊕ n∈
ZRn be a strongly graded ring of type Z, where Z is the ring of integers. We always assume
that R0, the degree zero part, is a prime Goldie ring with its quotient ring Q0 and C0={c∈ …
maximal order, then so is R. We define a concept of Z-invariant maximal order and show R0
is a Z-invariant maximal order if and only if R is a maximal order. We provide examples of R0
which are Z-invariant maximal orders but not maximal orders. 1 Introduction Let R=⊕ n∈
ZRn be a strongly graded ring of type Z, where Z is the ring of integers. We always assume
that R0, the degree zero part, is a prime Goldie ring with its quotient ring Q0 and C0={c∈ …
Abstract
Let R=⊕ n∈ ZRn be a strongly graded ring of type Z. In [6], it is shown that if R0 is a maximal order, then so is R. We define a concept of Z-invariant maximal order and show R0 is a Z-invariant maximal order if and only if R is a maximal order. We provide examples of R0 which are Z-invariant maximal orders but not maximal orders.
1 Introduction Let R=⊕ n∈ ZRn be a strongly graded ring of type Z, where Z is the ring of integers. We always assume that R0, the degree zero part, is a prime Goldie ring with its quotient ring Q0 and C0={c∈ R0| c is regular in R0}, which is a regular Ore set of R and the ring of fractions Qg of R at C0 has the following properties:
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