Cancellation and hopficity in direct products
نویسندگان
چکیده
منابع مشابه
Cancellation of direct products of digraphs
We investigate expressions of form A×C ∼= B×C involving direct products of digraphs. Lovász gave exact conditions on C for which it necessarily follows that A ∼= B. We are here concerned with a different aspect of cancellation. We describe exact conditions on A for which it necessarily follows that A ∼= B. In the process, we do the following: Given an arbitrary digraph A and a digraph C that ad...
متن کاملCancellation in Direct Sums of Groups
5. L. K. Hua, A note on the total matrix ring over a non-commutative field, Annales de la Société Polonaise de Mathématique vol. 25 (1952) pp. 188-198. 6. N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 479-502. 7. F. Kasch, Invariante Untermoduln des Endomorphismenrings eines Vektorraums, Archiv der Mathematik vol. 4 (1953) pp. 182-190. ...
متن کاملCoupled Cells: Wreath Products and Direct Products
In this note we discuss the structure of systems of coupled cells (which we view as systems of ordinary differential equations) where symmetries of the system are obtained through the group G of global permutations of the cells and the group L of local internal symmetries of the dynamics in each cell. We show that even when the cells are assumed to be identical with identical coupling, the way ...
متن کاملCancellation properties of products of graphs
This note extends results of Fernández, Leighton, and López-Presa on the uniqueness of r roots for disconnected graphs with respect to the Cartesian product to other products and shows that their methods also imply new cancelation laws.
متن کاملCancellation of digraphs over the direct product
In 1971 Lovász proved the following cancellation law concerning the direct product of digraphs. If A, B and C are digraphs, and C admits no homomorphism into a disjoint union of directed cycles, then A × C ∼= B × C implies A ∼= B. On the other hand, if such a homomorphism exists, then there are pairs A ≁= B for which A×C ∼= B×C . This gives exact conditions on C that governwhether cancellation ...
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: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90171-0