Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...

Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...

Let D ≡ 7 mod 8 be a positive squarefree integer, and let hD be the ideal class number of ED = Q( √−D). Let d ≡ 1 mod 4 be a squarefree integer relatively prime to D. Then for any integer k ≥ 0 there is a constant M = M(k), independent of the pair (D, d), such that if (−1)k = sign(d), (2k + 1, hD) = 1, and √ D > 12 π d(log |d|+ M(k)), then the central L-value L(k + 1, χ D,d ) > 0. Furthermore, ...