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【期刊论文】Dualizing Complexes over Noncommutative Local Rings
吴泉水, Q.-S. Wu, J.J. Zhang
Journal of Algebra 239, 513-548 (2001),-0001,():
-1年11月30日
We prove an existence theorem for dualizing complexes over noncommutative noetherian complete semilocal algebras, which generalizes Van den Bergh's existence theorem in the graded case. Using the dualizing complex, noncommutative versions of Bass theorem and the no-holes theorem are proved. We also prove that noetherian complete semilocal algebras satisfying polynomial identities are catenary.
semilocal algebra, PI algebra, local cohomology, dualizing complex, Bass theorem, no-holes theorem
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【期刊论文】Homological Identities for Noncommutative Rings
吴泉水, Q.-S. Wu, J.J. Zhang
Journal of Algebra 242, 516-535 (2001),-0001,():
-1年11月30日
The Auslander–Buchsbaum formula and Bass's theorem are proved for a class of nonlocal, noncommutative algebras (including certain affine PI Hopf algebras). We also show that each filtered noetherian affine PI Hopf algebra has finite injective dimension, which partially answers a question of Brown.
Auslander-Buchsbaum formula, Bass', s theorem, AS-Gorensteinness, Hopf algebra.,
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【期刊论文】Some Homological Invariants of Local PI Algebras
吴泉水, Q.S. Wu, J.J. Zhang
Journal of Algebra 225, 904-935 (2000),-0001,():
-1年11月30日
semilocal PI algebra, Auslander-Buchsbaum formula, depth, local cohomology, Morita duality.,
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【期刊论文】HOMOLOGICAL INTEGRAL OF HOPF ALGEBRAS
吴泉水, D.-M. LU, Q.-S. WU AND J.J. ZHANG
,-0001,():
-1年11月30日
The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The generalization of Maschke's theorem and homological integrals are the keys to study noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.
Hopf algebra,, homological integral,, Gorenstein property,, regularity,, Gelfand-Kirillov dimension,, integral order,, integral quotient,, PI degree.,
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