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Products in almost f -algebras

Karim Boulabiar (2000)

Commentationes Mathematicae Universitatis Carolinae

Let A be a uniformly complete almost f -algebra and a natural number p { 3 , 4 , } . Then Π p ( A ) = { a 1 a p ; a k A , k = 1 , , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 a A } as positive cone.

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...

Putting together Lukasiewicz and product logics.

Francesc Esteva, Lluis Godo (1999)

Mathware and Soft Computing

In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.

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