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Complexes Over a Complete Algebra of Quotients

  • Krishna Tewari (a1)

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Let R be a commutative ring with unit and A be a unitary commutative R-algebra. Let As be a generalized algebra of quotients of A with respect to a multiplicatively closed subset S of A. If (A) and (As ) denote the categories of complexes and their homomorphisms over A and As respectively, then one easily sees that there exists a covariant functor T: (A) → (AS) such that T is onto and T(X, d) is universal over As whenever (X, d) is universal over A. Actually the category (AS) is equivalent to a subcategory of (A) where contains all those complexes (X, d) over A such that for each s in S, the module homomorphism ϕs: xsx of Xn into itself is one-one and onto for each n ⩾ 1.

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References

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1. Bourbaki, N., Algèbre commutative, Chap. I (Paris, 1961).
2. Bourbaki, N., Algèbre, Chap. II (Paris, 1955).
3. Cartan, H. and Eilenberg, S., Homologuai algebra (Princeton, 1956).
4. Chevalley, C., Fundamental concepts of algebra (New York), 1956.
5. Kähler, E., Algebra und Differentialrechnung Bericht über die Mathematiker-Tagung in Berlin vom 14. bis 18. Januar 1953 (Berlin, 1954).
6. Lambek, J., On the structure of semi-prime rings and their rings of quotients, Can. J. Math., 13 (1961), 392417.
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Complexes Over a Complete Algebra of Quotients

  • Krishna Tewari (a1)

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