Genera and arithmetic genera of commutative rings
نویسندگان
چکیده
منابع مشابه
Genera of Arithmetic Fuchsian Groups
Introduction. The fundamental invariant of a Riemann surface is its genus. In this paper, using arithmetical means, we calculate the genus of certain Riemann surfaces defined by unit groups in quaternion algebras. First we recall a well-known general construction of Riemann surfaces. The group SL2(R) acts on the upper half-plane H by Möbius transformations. If G is a Fuchsian group, that is, a ...
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AS e 5m_2(S), AE e O5m-2(E) and (As)r = (AE)r; thus A -* AS + AE iS a linear mapping of Om -2(9ON) into (M. It follows from the proposition (II) that, for every element a, + a2 of 5, there exists one and only one element A Of O5m-2() with AE = a2. This element A satisfies (a, As)r= a2r (AE)r = 0, while r = ES is a hyperplane section of S. Hence, by the proposition (I), we get AS = a,. Thus we s...
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* This work has been partly supported by Army Air Force's contracts. 1 Dresher, M., Karlin, S., and Shapley, L. S., Ann. Math. Studies, 24, 161-180, (1950). 2 Dresher, M., and Karlin, S., Ibid., 28, 75-86, (1953). 3 McKinsey, J. C. C., Introduction to the Theory of Games, McGraw-Hill Book Co., New York, 1952, pp. 254, 277-290. 4 Borel, E., three short papers "On Games That Involve Chance and th...
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It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...
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We prove that the existence of the integral closure of a countable commutative ring R in a countable commutative ring S is equivalent to Arithmetical Comprehension (over RCA0). We also show that i) the Lying Over ii) the Going Up theorem for integral extensions of countable commutative rings and iii) the Going Down theorem for integral extensions of countable domains R ⊂ S, with R normal, are p...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1987
ISSN: 0018-2079
DOI: 10.32917/hmj/1206130188