The Ritt problem asks if there is an algorithm that tells whether one prime differential ideal is contained in another one if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we show that it is equivalent to testing if a differential polynomial is a zero divisor modulo a radical differential ideal. The technique used in the pro...

In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...

All rings in this paper are assumed to be commutative with identity, and they will generally also be Noetherian. In several recent papers the asymptotic theory of ideals in Noetherian rings has been introduced and developed. In this new theory the roles played in the standard theory by associated primes, i?-sequences, classical grade, and Cohen-Macaulay rings are played by, respectively, asympt...

We prove that the associated variety of a Poisson prime ideal of the centre of a symplectic reflection algebra at parameter t = 0 is irreducible.

s of papers presented at the meeting follow. Abstracts whose titles are followed by "t" were presented by title. Mrs. Lehmer was introduced by the Associate Secretary, Mr. Rail by Professor Lonseth, Professor Nash by Professor W. T. Martin, and Mr. Krabble by Professor C. B. Morrey. ALGEBRA AND THEORY OF NUMBERS 5SSt. W. E. Barnes: Primal ideals in noncommutative rings. In any associative ring ...

For a commutative ring R, let Nil(R) be the set of all nilpotent elements of R, Z(R) be the set of all zero divisors of R, T (R) be the total quotient ring of R, and H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R ∈ H, let φ : T (R) −→ RNil(R) such that φ(a/b) = a/b for every a ∈ R and b ∈ R\Z(R). A ring R is called a ZPUI ring if every proper ideal of R...

In reading, lexical form-form relations may be more reliable than form-meaning relations. Accordingly, phonological forms (activated by graphic forms) become actual constituents, rather than addenda, of word identification. These considerations suggest that access to phonological forms can precede meaning access in single-word reading in many circumstances. The time course of form and meaning a...

Proof. First note that the zero element of the ring R/I is 0 + I = I and that a + I = I if and only if a ∈ I. Now suppose that I ⊆ R is a prime ideal and consider nonzero cosets a+ I and b+ I in R/I (i.e. consider a 6∈ I and b 6∈ I). Since I is prime this implies that ab 6∈ I, hence ab + I 6= I and we conclude that R/I is an integral domain. Conversely, let R/I be an integral domain and conside...

One of the sciences used in digital security systems is cryptography. Cryptography closely related to integer system, especially prime numbers. Prime numbers themselves have been abstracted a lot. form abstraction ideal. Previous studies proven that an Ideal said be ideal on if and only I constructed by element. Other also shown how develops. them research result Dauns, where developed submodul...