The Jacobson-Bourbaki Theorem for division rings was formulated in terms of corings by Sweedler in [14]. Finiteness conditions hypotheses are not required in this new approach. In this paper we extend Sweedler’s result to simple artinian rings using a particular class of corings, comatrix corings. A Jacobson-Bourbaki like correspondence for simple artinian rings is then obtained by duality.

We introduce the notions of Jacobson radical of a Γ−semiring and semisimple Γ−semiring and characterize them via operator semirings. AMS Mathematics Subject Classification (2000): 16Y60, 16Y99, 20N10

The study of Hamiltonian graphs began with Dirac’s classic result in 1952. This was followed by that of Ore in 1960. In 1984 Fan generalized both these results with the following result: If G is a 2-connected graph of order n and max{d(u), d(v)}≥n/2 for each pair of vertices u and v with distance d(u, v)=2, then G is Hamiltonian. In 1991 Faudree–Gould–Jacobson–Lesnick proved that if G is a 2-co...

Given a quasi-reductive algebraic supergroup G , we use the theory of semisimplifications symmetric monoidal categories to define functor ? x : Rep ( ) ? O S p 1 | 2 associated any given element ? Lie ¯ . For nilpotent elements show that can be defined using Deligne filtration We this approach prove an analogue Jacobson-Morozov Lemma for supergroups. Namely, give necessary and sufficient condit...

For a graph G = (V, E) and integer p, a p-intersection representation is a family = {Sx: x E V} of subsets of a set S with the property that IS, n S,l 2 p {u, u } E E. It is conjectured in 111 that 8,(G) I B(K,,/2,,,/2)(1 + o(1)) holds for any graph with n vertices. This is known to be true for p = 1 by [41. In [ I ] , O(K,,/2,,,/2) 1 (n2 + (2p l)n)/4p is proved for any n and p. Here, we show t...

From the Department of Pediatric and Adolescent Medicine, Mayo Clinic, Rochester, Minn (Dr Jacobson); AcademyHealth, Washington, DC (Dr Fairbrother); Department of Pediatrics, Tufts Medical Center, Boston, Mass (Dr Sheldrick); and Department of Pediatrics, University of California Los Angeles, Calif (Dr Szilagyi) Conflict of Interest: The authors declare that they have no conflict of interest. ...

A plausible conjecture states that an element of the Jacobson radical of the endomorphism ring of an abelian p-group increases the height of any non-zero element of the socle. I construct a counter-example.