A note on homomorphisms of Hilbert algebras
We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-i...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202011134 |
| Summary: | We give a representation theorem for Hilbert algebras by
means of ordered sets and characterize the homomorphisms of
Hilbert algebras in terms of applications defined between the
sets of all irreducible deductive systems of the associated
algebras. For this purpose we introduce the notion of
order-ideal in a Hilbert algebra and we prove a separation
theorem. We also define the concept of semi-homomorphism as
a generalization of the similar notion of Boolean algebras and we
study its relation with the homomorphism and with the
deductive systems. |
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| ISSN: | 0161-1712 1687-0425 |