Let k > 9 be an even integer and p a prime with p > 2k− 2. Let f be a newform of weight 2k− 2 and level SL2(Z) so that f is ordinary at p and ρ f,p is irreducible. Under some additional hypotheses, we prove that ordp(Lalg(k, f)) ≤ ordp(#S), where S is the Pontryagin dual of the Selmer group associated to ρ f,p ⊗ ε1−k with ε the p-adic cyclotomic character. We accomplish this by first constructi...

Flat iteration is a variation on the original binary version of the Kleene star operation P Q, obtained by restricting the rst argument to be a sum of atomic actions. It generalizes pre x iteration, in which the rst argument is a single action. Complete nite equational axiomatizations are given for ve notions of bisimulation congruence over basic CCS with at iteration, viz. strong congruence, b...

We describe the image of the absolute Galois group acting on the pro-l completion of the fundamental group of the Gm minus Nth roots of unity. We relate the structure of the image with geometry and topology of modular varieties for the congruence subgroups 01(m; N ) of GLm(Z) for m = 1, 2, 3 . . . .

We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone cohomology, such that the cohomology group in dimension one is the group of equivalence classes of extensions.

the aim of the present research was to investigate the relationship between the components of organizational intelligence and organizational culture in physical education general office and offices in east azerbaijan province. the present research was a descriptive – correlation one and performed as a field. the statistical population consisted of the staff of physical education general office ...

Nearly twenty years ago, two of the authors wrote a paper on congruence lattices of semilattices [9]. The problem of finding a really useful characterization of congruence lattices of finite semilattices seemed too hard for us, so we went on to other things. Thus when Steve Seif asked one of us at the October 1990 meeting of the AMS in Amherst what we had learned in the meantime, the answer was...

Congruence Closure and Applications Congruence closure algorithms for solving word problems for finitely pre-sented algebras have also been used in combining decision procedures. Onthe other hand, congruence closure can itself be looked upon as a combina-tion problem. Taking this view leads us to define the notion of an abstractcongruence closure. We present a completion based d...

A congruence relation θ on an algebra A is fully invariant if every endomorphism of A preserves θ. A congruence θ is verbal if there exists a variety V such that θ is the least congruence of A such that A/θ ∈ V. Every verbal congruence relation is known to be fully invariant. This paper investigates fully invariant congruence relations that are verbal, algebras whose fully invariant congruences...