Recently Yehuda Rav has given the concept of Semi prime ideals in a general lattice by generalizing the notion of 0-distributive lattices. In this paper we study several properties of these ideals in a general nearlattice and include some of their characterizations. We give some results regarding maximal filters and include a number of Separation properties in a general nearlattice with respect...

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 ...

Let 9t and © be commutative rings such that © contains, and has the same identity element as, 9Î. If p and $ are prime ideals in SK and © respectively such that ^P\9t = p then we shall say that $ lies over, or contracts to, p. If over every prime ideal in dt there lies a prime ideal in ©, we shall say that the "lying-over" theorem holds for the pair of rings 9Î and ©. Suppose now that q and p a...

One can check that there exists a lattice which is non trivial, Boolean, and strict. Let X be a set. Observe that there exists a family of subsets of X which is finite and non empty. Let S be a 1-sorted structure. One can check that there exists a family of subsets of S which is finite and non empty. Let L be a non trivial upper-bounded non empty poset. Note that there exists a filter of L whic...

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset f of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if f is two-valued, f(0) = 1, and the set of all x in S such that f(x) = 1 is a prime (left) right h-ideal of S. Fina...

The concept of  -ideals is introduced in an Almost Distributive lattice(ADL) with respect to a congruence and the properties of  -ideals are studied. Derived a set of equivalent conditions for a  -ideal to become a  -prime ideal.

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

For a ring endomorphism α and an α-derivation δ, we introduce α-compatible ideals which are a generalization of α-rigid ideals and study the connections of the prime radical and the upper nil radical of R with the prime radical and the upper nil radical of the Ore extension R[x;α, δ] and the skew power series R[[x;α]]. As a consequence we obtain a generalization of Hong, Kwak and Rizvi, 2005.

We show that the regularity of monomial ideals of K[x1, . . . , xn] (K being a field), whose associated prime ideals are totally ordered by inclusion is upper bounded by a linear function in n.

We provide methods to do explicit calculations in a polynomial ring in finitely many variables over a field. We develop algorithms to compute quotients of ideals, the radical of an ideal and a primary decomposition of an ideal. We also present methods to solve explicit tasks such as testing for prime ideals or identical ideals.