Displaying similar documents to “Boolean semirings”

Representation of a Boolean algebra by its triangular norms.

Suryansu Ray (1997)

Mathware and Soft Computing

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Given a complete and atomic Boolean algebra B, there exists a family tau of triangular norms on B such that, under the partial ordering of triangular norms, tau is a Boolean algebra isomorphic to B, where gamma is the set of all atoms in B. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that tau is not unique for B and that, for such a representation,...

Boolean structure of triangular norms.

Seyed Abbas Ziaie, S. Ray, Mashallah Mashinchi, Rasool Kamran (1999)

Mathware and Soft Computing

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In this note results obtained by S.Ray (1997) on representation of a Boolean algebra by its triangular norms are generalized.

Multiplicatively idempotent semirings

Ivan Chajda, Helmut Länger, Filip Švrček (2015)

Mathematica Bohemica

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Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive...

On Semi-Boolean-Like Algebras

Antonio Ledda, Francesco Paoli, Antonino Salibra (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra 𝐀 with constants 0 , 1 is Boolean-like in case for all a A the congruences θ a , 0 and θ a , 1 are complementary factor congruences of 𝐀 . We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue...

A characterization of complete atomic Boolean algebra.

Francesc Esteva (1977)

Stochastica

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In this note we give a characterization of complete atomic Boolean algebras by means of complete atomic lattices. We find that unicity of the representation of the maximum as union of atoms and Lambda-infinite distributivity law are necessary and sufficient conditions for the lattice to be a complete atomic Boolean algebra.