Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...

A positive semi-definite Euclidean action for arbitrary four-topologies can be constructed by adding appropriate Yang-Mills and topological terms to the Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables. Moreover, on-shell, the (anti)self-dual sector of the new theory corresponds precisely to all Einstein manifolds in four dimensions. The Lorentzian signature action, and i...

We construct the H-von Neumann regular radical for H-module algebras and show that it is an H-radical property. We obtain that the Jacobson radical of twisted graded algebra is a graded ideal. For twisted H-module algebra R, we also show that rj(R#σH) = rHj(R)#σH and the Jacobson radical of R is stable, when k is an algebraically closed field or there exists an algebraic closure F of k such tha...

Thomas P. Mackey is Interim Dean in the Center for Distance Learning at SUNY Empire State College; e-mail: [email protected]. Trudi E. Jacobson is Head of User Education Programs in the University Libraries of University at Albany, SUNY; e-mail: [email protected]. © Thomas P. Mackey and Trudi E. Jacobson Social media environments and online communities are innovative collaborative te...

101, 415-425 9 de Rrabander, M., Nuydens, K., Ishihara, A,, Holifield, H., Jacobson, K. and Geerts. H. (1991) J. Cell Hiol. 112. 111-124 10 Lee, G. M., Ishihara, A. and Jacobson, K. A. (1991) Proc. Natl. Acad. Sci. U.S.A. 88, 6274-6278 11 Kusumi, A., Sako, Y. and Yamamoto, M. (1903) Biophys. J. 65.202 1-2040 12 Shotton, L). M. (1991) in New Techniques of Optical Microscopy and Microspectroscopy...

Gould, R.J. and V. RodI, On isomorphic subgraphs, Discrete Mathematics 118 (1993) 2599262. We prove that every 3-uniform hypergraph with 4 edges contain two edge disjoint isomorphic subgraphs with at least L&A J edges, This answers a question of Erdiis, Path and Pyber. Recently, the following question was independently raised by MS. Jacobson (personal communication) and J. Schonheim (see Cl]). ...