In this paper, we show that the Alperin–McKay conjecture holds for 2-blocks of maximal defect. A major step in proof is verification principal 2-block groups Lie type odd characteristic AM-good prime 2.

Long binary sequences related to cyclic difference sets are investigated. Among all known constructions of cyclic difference sets we show that only sequences constructed from Hadamard difference sets can have an asymptotic nonzero merit factor. Maximal length shift register sequences, Legendre, and twin-prime sequences are all constructed from Hadamard difference sets. We prove that the asympto...

In this paper a bijection between the set of prime ideals of a Leavitt path algebra L K (E) and a certain set which involves maximal tails in E and the prime spectrum of K[x, x −1 ] is established. Necessary and sufficient conditions on the graph E so that the Leavitt path algebra L K (E) is primitive are also found.

It is shown that a squarefree principal Borel ideal satisfies the persistence property for the associated prime ideals. For the graded maximal ideal we compute the index of stability with respect to squarefree principal Borel ideals and determine their stable set of associated prime ideals.

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices. Define...

n(n + d) . . . (n + (k − 1)d) = by (1.1) in positive integers n, k ≥ 2, d > 1, b, y, l ≥ 3 with l prime, gcd(n, d) = 1 and P (b) ≤ k. We write d = D1D2 (1.2) where D1 is the maximal divisor of d such that all prime divisors of D1 are congruent to 1 ( mod l). Thus D1 and D2 are relatively prime positive integers such that D2 has no prime divisor which is congruent to 1 (mod l). Shorey [Sh88] pro...

‎In this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎We show that if F is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎Rad(F)=F‎. ‎We proved the extension theorem for radical of filters in residuated lattices‎. ‎Also‎, ‎we study the radical‎ ‎of filters in linearly o...

Byun, H.L. and S. Watson, Prime and maximal ideals in subrings of C(X), Topology and its Applications 40 (1991) 45-62. The structure of ideals in the ring C(X) of continuous functions on a completely regular space X and its subring C*(X) consisting of the bounded functions is well known. In this paper we study the prime and maximal ideals in subrings A(X) of C(X) that contain C*(X). We show tha...

Abstract Let $E/\mathbb {Q}$ be an elliptic curve. For a prime p of good reduction, let $r(E,p)$ the smallest non-negative integer that gives x -coordinate point maximal order in group $E(\mathbb {F}_p)$ . We prove unconditionally $r(E,p)> 0.72\log \log p$ for infinitely many , and 0.36 under assumption Generalized Riemann Hypothesis. These can viewed as curve analogues classical lower bound...

Abstract We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study monomials canonical bases, K -theoretic for quiver representations, and some maximal prime tropical flag varieties.