All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 83

Showing per page

On annihilators in BL-algebras

Yu Xi Zou, Xiao Long Xin, Peng Fei He (2016)

Open Mathematics

In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties...

On connections between information systems, rough sets and algebraic logic

Stephen Comer (1993)

Banach Center Publications

In this note we remark upon some relationships between the ideas of an approximation space and rough sets due to Pawlak ([9] and [10]) and algebras related to the study of algebraic logic - namely, cylindric algebras, relation algebras, and Stone algebras. The paper consists of three separate observations. The first deals with the family of approximation spaces induced by the indiscernability relation for different sets of attributes of an information system. In [3] the family of closure operators...

Prime ideals in 0-distributive posets

Vinayak Joshi, Nilesh Mundlik (2013)

Open Mathematics

In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in which atoms are dually distributive. Further, it is proved that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime. The second section focuses on the characterizations of (minimal) prime ideals in pseudocomplemented posets. The third section deals with the generalization...

Properties of relatively pseudocomplemented directoids

Ivan Chajda, Miroslav Kolařík, Filip Švrček (2011)

Mathematica Bohemica

The concept of a relatively pseudocomplemented directoid was introduced recently by the first author. It was shown that the class of relatively pseudocomplemented directoids forms a variety whose axiom system contains seven identities. The aim of this paper is three-fold. First we show that these identities are not independent and their independent subset is presented. Second, we modify the adjointness property known for relatively pseudocomplemented semilattices in the way which is suitable for...

Pseudocomplemented and Stone Posets

Ivan Chajda (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We show that every pseudocomplemented poset can be equivalently expressed as a certain algebra where the operation of pseudocomplementation can be characterized by means of remaining two operations which are binary and nullary. Similar characterization is presented for Stone posets.

Pseudocomplemented directoids

Ivan Chajda (2008)

Commentationes Mathematicae Universitatis Carolinae

Directoids as a generalization of semilattices were introduced by J. Ježek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras.

Pseudocomplements in sum-ordered partial semirings

Jānis Cīrulis (2007)

Discussiones Mathematicae - General Algebra and Applications

We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...

Currently displaying 41 – 60 of 83