Characterization of binary polynomials of idempotent algebras |
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Authors: | Yu M Movsisyan J Pashazadeh |
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Institution: | 1. Yerevan State University, Yerevan, Armenia 2. Islamic Azad University, Bonab branch, Bonab, Iran
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Abstract: | In this paper, we characterize the set of all binary algebraic (or polynomial) operations of an idempotent algebra that has at least one r-ary algebraic operation, (r ≥ 2), depending on every variable such that there is no an (r+2)-ary algebraic operation depending on at least (r+1) variables. We prove that this set forms a finite Boolean algebra, and then we characterize this Boolean algebra. |
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