the concepts of fuzzy semi-ideals of r with respect to h≤r and generalized fuzzy quotient rings are introduced. some properties of fuzzy semiideals are discussed. finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

The purpose of this article is to obtain some new infinite families of Toeplitz matrices, 7-matrices and generalized Pascal triangles whose leading principal minors form the Fibonacci, Lucas, Pell and Jacobsthal sequences. We also present a new proof for Theorem 3.1 in [R. Bacher. Determinants of matrices related to the Pascal triangle. J. Théor. Nombres Bordeaux, 14:19–41, 2002.].

An analytic proof of an evaluation theorem for the “convolution”type double L-values of non-principal characters is given. Along the way, Dirichlet character analogues of generalized single and double polylogarithms are defined. The monodromies of these functions play a pivotal role.

Abstract We present the generalized optical theorem and its applications with special emphasis on roles of bound states. First, we prove which gives a necessary sufficient condition for function $\langle {\bf {\it k}^{\prime}} | T k}} \rangle$ two variables $\ k}}^{\prime }$ ${\bf k}}$ to be physically acceptable as half-on-shell T-matrix, i.e., have an underlying Hermitian potential V. Second,...

We recall that Theorem 1.3 allows us to define the ideal class group of a Dedekind domain, and in particular of a ring of integers, as the group of fractional ideals modulo the subgroup of principal ideals. We will prove that in the case of a ring of integers, the ideal class group is finite. In fact, we will shortly give a stronger statement due to Minkowski. Using similar techniques, we will ...