Isomorphism of complete local noetherian rings and strong approximation

Strong Reductions and Isomorphism of Complete Sets

We study the structure of the polynomial-time complete sets for NP and PSPACE under strong nondeterministic polynomial-time reductions (SNP-reductions). We show the following results. • If NP contains a p-random language, then all polynomial-time complete sets for PSPACE are SNP-isomorphic. • If NP ∩ co-NP contains a p-random language, then all polynomial-time complete sets for NP are SNP-isomo...

Ultraproducts of Noetherian Local Rings: Properties and Applications

The present proposal is in part a continuation of the NSF Research Proposal Definability, Constructibility and Transfer (DMS-0100778/DMS-0302248 in the amount of $69,276; project details are given in §4.3 and the introduction to §5). Whereas the latter proposal was submitted via the division Foundations, in view of the underlying tools stemming from model-theory, the present proposal is cast en...

Artinian and Noetherian Rings

Fully Bounded Noetherian Rings

Let i : A → R be a ring morphism, and χ : R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1 R) = 1 A. If R is a Frobenius A-ring, then we can define a trace map tr : A → A R. If there exists an element of trace 1 in A, then A is right FBN if and only if A R is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover resul...

ساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings

فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...