منابع مشابه
Generically stable, ω-categorical groups and rings
In two recent papers with Krzysztof Krupi´nski, we proved that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite. During the lecture, after a brief overview of well-known results on ω-categorical groups and rings, I will explain the main ideas of the proofs of our results.
متن کاملOn ω-categorical, generically stable groups and rings
We prove that every ω-categorical, generically stable group is nilpotent-byfinite and that every ω-categorical, generically stable ring is nilpotent-by-finite.
متن کاملOn ω-categorical groups and rings with NIP
We show that ω-categorical rings with NIP are nilpotent-by-finite. We prove that an ω-categorical group with NIP and fsg is nilpotent-by-finite. We also notice that an ω-categorical group with at least one strongly regular type is abelian. Moreover, we get that each ω-categorical, characteristically simple p-group with NIP has an infinite, definable abelian subgroup. Assuming additionally the e...
متن کاملNotes on totally categorical theories
Cherlin, Harrington and Lachlan’s paper on ω0-categorical, ω0-stable theories ([CHL]) was the starting point of geometrical stability theory. The progress made since then allows us better to understand what they did in modern terms (see [PI]) and also to push the description of totally categorical theories further, (see [HR1, AZ1, AZ2]). The first two sections of what follows give an exposition...
متن کاملCategorical representations of categorical groups
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1979
ISSN: 0021-8693
DOI: 10.1016/0021-8693(79)90230-8