Scientiae Mathematicae Japonicae · Scientiae Mathematicae Japonicae Abstract. Let R = n2ZR n be a...
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Scientiae Mathematicae Japonicae Abstract. Let R = ⊕ n∈Z Rn 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. Key words and phrases. Graded ring; maximal order; prime Goldie ring; hereditary Noetherian prime ring. STRONGLY GRADED RINGS WHICH ARE MAXIMAL ORDERS Hidetoshi Marubayashi 1 , Sri Wahyuni 2 , Indah Emilia Wijayanti 3 , Iwan Ernanto 4 Received December 8, 2017
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Scientiae Mathematicae Japonicae
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 orderand show R0 is a Z-invariant maximal order if and only if R is a maximal order. Weprovide examples of R0 which are Z-invariant maximal orders but not maximal orders.
Key words and phrases. Graded ring; maximal order; prime Goldie ring; hereditary Noetherian primering.
STRONGLY GRADED RINGS WHICH ARE MAXIMAL ORDERS
Hidetoshi Marubayashi1, Sri Wahyuni2,Indah Emilia Wijayanti3, Iwan Ernanto4
Received December 8, 2017