Formal complexity of inverse semigroup rings
1990 ◽
Vol 41
(3)
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pp. 343-346
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A ring (R, *) with involution * is called formally complex if implies that all Ai are 0. Let (R, *) be a formally complex ring and let S be an inverse semigroup. Let (R[S], *) be the semigroup ring with involution * defined by . We show that (R[S], *) is a formally complex ring. Let (S, *) be a semigroup with proper involution *(aa* = ab* = bb* ⇒ a = b) and let (R, *′) be a formally complex ring. We give a sufficient condition for (R[S], *′) to be a formally complex ring and this condition is weaker than * being the inverse involution on S. We illustrate this by an example.
1967 ◽
Vol 67
(3)
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pp. 175-184
2016 ◽
Vol 94
(3)
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pp. 457-463
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1980 ◽
Vol 32
(6)
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pp. 1361-1371
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1988 ◽
Vol 110
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pp. 113-128
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1988 ◽
Vol 45
(3)
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pp. 372-380
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2008 ◽
Vol 85
(1)
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pp. 75-80
2007 ◽
Vol 83
(3)
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pp. 357-368
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