Factoring out the socle of a Gorenstein ring
نویسندگان
چکیده
منابع مشابه
On Property (A) and the socle of the $f$-ring $Frm(mathcal{P}(mathbb R), L)$
For a frame $L$, consider the $f$-ring $ mathcal{F}_{mathcal P}L=Frm(mathcal{P}(mathbb R), L)$. In this paper, first we show that each minimal ideal of $ mathcal{F}_{mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $mathcal{F}_{mathcal P}$-completely regular frame, then the socle of $ mathcal{F}_{mathcal P}L$ consists of those $f$...
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A topoframe, denoted by $L_{ tau}$, is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in$L$. $f$-ring $mathcal{R}(L_{ tau})$ is equal to the set $${fin Frm(mathcal{P}(mathbb R), L): f(mathfrak{O}(mathbb R))subseteq tau} .$$ In this paper, for every complemented element $ain L$ with $a, a'...
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We give an exposition and generalization of Orlov’s theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary non-commutative right noetherian ring of finite global dimension. A short treatment of some foundations for local cohomology and Grothendieck duality at this ...
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For a generic W algebra, we give an algorithmic procedure for factoring out all fields of dimension 1/2, both bosonic and fermionic, and some fields of dimension 1. This generalizes and makes more explicit the GoddardSchwimmer theorem for free fermions. We also show how the induced gravity theory for the original W algebra containing the free fields relates to the theory where the fields are fa...
متن کاملThe Poincaré Series of Modules over Generic Artinian Gorenstein Algebras of Even Socle Degree
Let Q = k[[x1, . . . , xn]] be the power series ring over a field k. Artinian Gorenstein quotients R = Q/I whose unique maximal ideal m satisfies ms 6= 0 = ms+1 are in correspondence via the Macaulay inverse system with degree s polynomials in n variables. Bøgvad constructed examples for which the Poincaré series of k over R is irrational. When s is even, we prove that such examples are rare. M...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90191-6