The Royden ideal boundary of a domain is the set of all points in the maximal ideal space of the domain's Royden algebra that do not lie in the domain. Elements of the Royden ideal boundary can be characterized as nets convergent in both the weak and Euclidean topologies that have no subnet which is a sequence. As with other function algebras, boundary bers can be deened as subsets of all point...

It is well-known that two modular forms on the same congruence subgroup and of the same weight, with coefficients in the integer ring of a number field, are congruent modulo a prime ideal in this integer ring, if the first B coefficients of the forms are congruent modulo this prime ideal, where B is an effective bound depending only on the congruence subgroup and the weight of the forms. In thi...

In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal in terms of its characteristic set under an arbitrary ranking, which shows the Jacobi bound conjecture holds in this case. Apart from the order bound, we als...

In this paper, we are interested in the question of separating two characters of the absolute Galois group of a number field K, by the Frobenius of a prime ideal p of OK . We first recall an upper bound for the norm N(p) of the smallest such prime p, depending on the conductors and on the degrees. Then we give two applications: (i) find a prime number p for which P (mod p) has a certain type of...

in this paper we define the notions of ultra and involution ideals in bck-algebras. then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. specially, we show that in a bounded implicative bck-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower bck-semilattice, the notions of...

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...

Let O be an order in the number field K. When O 6= OK , O is Noetherian and onedimensional, but is not integrally closed, so it has at least one nonzero prime ideal that’s not invertible and O doesn’t have unique factorization of ideals. That is, some nonzero ideal in O does not have a unique prime ideal factorization. We are going to define a special ideal in O, called the conductor, that is c...

In this paper, we initiate the study of prime bi-ideals (fuzzy bi-ideals) in semirings. We define strongly prime, prime, semiprime, irreducible and strongly irreducible bi-ideals in semirings. We also define strongly prime, semiprime, irreducible, strongly irreducible fuzzy bi-ideals of semirings. We characterize those semirings in which each bi-ideal (fuzzy bi-ideal) is prime (strongly prime).

‎in this paper‎, ‎we introduce the notion of the radical of a $pmv$-algebra $a$ and we charactrize radical $a$ via elements of $a$‎. ‎also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $pmv$-algebras‎. ‎several characterizations of this radical is given‎. ‎we define the notion of a semimaximal $cdot$-ideal in a $pmv$-algebra‎. ‎finally we show that $a/i$ has no nilpotent elemen...

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.