Introduction and summary. In the theory of non-commutative rings certain distinguished subrings, one-sided and two-sided ideals, play the important roles. Ideals combine under crosscut, union and multiplication and hence are an instance of a lattice over which a non-commutative multiplication is defined.f The investigation of such lattices was begun by W. Krull (Krull [3]) who discussed decompo...

Introduction. This article highlights some of the recent results in theoretical integer programming that have been obtained by studying integer programs using tools from commutative algebra and algebraic geometry. The main computational tool involved in the discussion here is the Gröbner basis of a special polynomial ideal called a toric ideal [30],[14]. For connections between Gröbner bases of...

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

The aim of this paper is to introduce power idealization filter topologies with respect to filter topologies and power ideals of lattice implication algebras, and to investigate some properties of power idealization filter topological spaces and their quotient spaces.

In this study, we present generalizations of the concept r-ideals in commutative rings with a nonzero identity. Let R be ring 0 ≠ 1 and L(R) lattice all ideals R. Suppose that ϕ:L(R) → ∪ {Ø} is function. A proper ideal I called ϕ-r-ideal if whenever ab ∈ Ann(a) = (0) imply b for each a,b addition to proven many properties ϕ-r-ideals, also examine ϕ-r-ideals trivial extension use them characteri...

Given a set X of “indeterminates” and a field F , an ideal in the polynomial ring R = F [X] is called conservative if it contains with any polynomial all of its monomials. The map S 7→ RS yields an isomorphism between the power setP (X) and the complete lattice of all conservative prime ideals of R. Moreover, the members of any system S ⊆ P (X) of finite character are in one-to-one corresponden...

We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean combinations. These properties include effective algebraic characterizations and lattice identities. In the main part of this paper we consider the following determini...

We give a new method to construct minimal free resolutions of all monomial ideals. This relies on two concepts: one is the well-known lcm-lattice ideal; other concept called Taylor basis, which describes how resolution can be embedded in resolution. An approximation formula for ideals also obtained.

With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M-valued L-topological spaces (i.e. (L,M)-topological spaces) and Idl(M)-valued L-topological spaces where Idl(M) is the complete lattice of all ideals of M. It is shown that the right adjoint functor provides a procedure of generating (L,M)-topologies from antitone families of (L,M)-topologies. ...