Rings, modules, and algebras in infinite loop space theory
نویسندگان
چکیده
منابع مشابه
2 3 M ar 2 00 4 RINGS , MODULES , AND ALGEBRAS IN INFINITE LOOP SPACE THEORY
We give a new construction of the algebraic K-theory of small permutative categories that preserves multiplicative structure, and therefore allows us to give a unified treatment of rings, modules, and algebras in both the input and output. This requires us to define multiplicative structure on the category of small permutative categories. The framework we use is the concept of multicategory, a ...
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Just over two years ago I wrote a summary of infinite loop space theory [37]. At the time, there seemed to be a lull in activity, with little immediately promising work in progress. As it turns out, there has been so much done in the interim that an update of the summary may be useful. The initial survey was divided into four chapters, dealing with additive infinite loop space theory, multiplic...
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Let A be an algebra over a commutative ring R. If R is noetherian and A◦ is pure in R, then the categories of rational left A-modules and right A◦-comodules are isomorphic. In the Hopf algebra case, we can also strengthen the Blattner– Montgomery duality theorem. Finally, we give sufficient conditions to get the purity of A◦ in R. © 2001 Academic Press
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The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl modules for the untwisted affine algebras. This identification allows us to use known results in the untwisted case to compute the dimensions and characters ...
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Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2006
ISSN: 0001-8708
DOI: 10.1016/j.aim.2005.07.007