Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case. In this paper, we establish some connections between the two approaches. In particular, we show that the corresponding code ideals are related by elimination...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

The purpose of this paper is to introduce and discuss the concept of T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal in a commutative ring . Our main aim in this paper is, generalization of theorems which have been proved in [6, 7, 11]. At first, T-rough sets introduced by Davvaz in [6]. By using the paper, we define a concept of T-rough ideal , T-rough quotient ideal an...

Let εD = v+u √ D be the fundamental unit of Z[ √ D] with Z being the ordinary integers, or maximal order, in the rational field Q. We prove that for any square-free integer D > 1, with D not dividing u, there exists a prime fD such that the relative class number HD(fD) = hf2 DD/hD = 1, where hD is the ideal class number of Z[ √ D] and hf2 DD is the ideal class number of Z[fD √ D], the order of ...

It is known that a k-term DNF can have at most 2k − 1 prime implicants and that this bound is sharp. We determine all k-term DNF having the maximal number of prime implicants. It is shown that a DNF is maximal if and only if it corresponds to a non-repeating decision tree with literals assigned to the leaves in a certain way. We also mention some related results and open problems.