In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

This paper examines critically the contributions of Cournot, Jevons and Walras as the founders of classical mathematical economics from a methodological standpoint. Advances in different economic schools and doctrines in the 19th century produced an environment of multi-dimensionality in economic analysis which was regarded by the pioneers of classical mathematical economists as a chaotic state...

We study in detail the algebra Sn in the title which is an algebra obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. The algebra Sn is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is proved that the classical Krull dimen...

We investigate the structure of prime ideals of finite height in polynomial extension rings of a commutative unitary ring R. We consider the question of finite generation of such prime ideals. The valuative dimension of prime ideals of R plays an important role in our considerations. If X is an infinite set of indeterminates over R, we prove that every prime ideal of R[X] of finite height is fi...

We develop a new approach of the quantum phase in an Hilbert space of finite dimension which is based on the relation between the physical concept of phase locking and mathematical concepts such as cyclotomy and the Ramanujan sums. As a result, phase variability looks quite similar to its classical counterpart, having peaks at dimensions equal to a power of a prime number. Squeezing of the phas...

Fix integers g ≥ 1 and N ≥ 3, and a prime p not dividing N . We show that the systems of Hecke eigenvalues occurring in the spaces of Siegel modular forms (mod p) of dimension g, level N , and varying weight, are the same as the systems occurring in the spaces of Siegel cusp forms with the same parameters and varying weight. In particular, in the case g = 1, this says that the Hecke eigensystem...

New properties of q-ary cyclotomic cosets modulo n = qm − 1, where q ≥ 3 is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of classical cyclic codes can be computed. As an application, new families of nonbinary Calderbank-Shor-Steane (CSS) quantum codes as well as new families of convolutional ...