In this paper, we initiate the study of prime bi-ideals (fuzzy bi-ideals) in semirings. We define strongly prime, prime, semiprime, irreducible and strongly irreducible bi-ideals in semirings. We also define strongly prime, semiprime, irreducible, strongly irreducible fuzzy bi-ideals of semirings. We characterize those semirings in which each bi-ideal (fuzzy bi-ideal) is prime (strongly prime).

We construct models for strongly-magnetized neutron star atmospheres composed of mid-Z elements (carbon, oxygen and neon) with magnetic fields B = 1012–1013 G and effective temperatures Teff = (1 − 5) × 106 K; this is done by first addressing the physics relevant to strongly-magnetized plasmas and calculating the equation of state and polarizationdependent opacities. We then obtain the atmosphe...

Let Z be a finite set of double points in P 1 × P 1 and suppose further that X, the support of Z, is arithmetically Cohen-Macaulay (ACM). The scheme Z is rarely ACM. In this note we present an algorithm, which depends only upon a combinatorial description of X, for the bigraded Betti numbers of I Z , the defining ideal of Z.

The Frohman Kania-Bartoszynska ideal is an invariant associated to a 3-manifold with boundary and a prime p ≥ 5. We give some estimates of this ideal. We also calculate this invariant for some 3-manifolds constructed by doing surgery on a knot in the complement of another knot. Let p = 2d+ 1 ≥ 5 be a prime and let O = { Z[ζp] if p ≡ −1 (mod 4) , Z[ζp, i] = Z[ζ4p] if p ≡ 1 (mod 4) . If M is an o...

Given distinct points p1, . . . , pr of a smooth variety V (over an algebraically closed field k) and positive integers mi, Z = m1p1 + · · · +mrpr denotes the subscheme defined locally at each point pi by I mi i , where Ii is the maximal ideal in the local ring OV,pi at pi of the structure sheaf. More briefly, we say Z is a fat point subscheme of V . In the case that V is P for some n, it is of...

The derivative of an ideal in a number ring is defined and the relation between the ideal derivative and the arithmetic derivative of a number in Z is discussed. Some simple ideal di↵erential equations are also studied. Further, the definition of the ideal derivative is extended to the derivative of a fractional ideal in a number ring. Again, the relation between the fractional ideal derivative...

We investigate the possibility of the existence of nonsparse strongly summable ultrafilters on certain abelian groups. In particular, we show that every strongly summable ultrafilter on the countably infinite Boolean group is sparse. This answers a question of Hindman, Steprāns and Strauss.

Building on recent phenomenology of γγ → ππ, we discuss the expectation for two photon production of longitudinal gauge boson pairs in SU(N) technicolor theories. The treatment involves a matching of dispersive techniques with the methodology of chiral perturbation theory. UMHEP-398 September 1993 e–mail: [email protected] e–mail: [email protected]

We prove the title. This characterizes the Jiang–Su algebra Z as the uniquely determined initial object in the category of strongly self-absorbing C-algebras.

The GMRES and Arnoldi algorithms, which reduce to the CR and Lanczos algorithms in the symmetric case, both minimize p(A)b over polynomials p of degree n. The difference is that p is normalized at z 0 for GMRES and at z x for Arnoldi. Analogous "ideal GMRES" and "ideal Arnoldi" problems are obtained if one removes b from the discussion and minimizes p(/l)II instead. Investigation of these true ...