Semisimplicity and the discriminator in bounded BCK-algebras |
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| Authors: | Antoni Torrens |
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| Affiliation: | 1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain
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| Abstract: | By means of an adaptation of a proof given by T. Kowalski in [16], we show that the members of a relative subvariety V of bounded BCK-algebras are all semisimple if and only if V is a variety and satisfies the identity | $ (x rightarrow y) rightarrow ((x^n rightarrow 0) rightarrow y) rightarrow y) approx 1,,{rm for,some},n > 0. $ (x rightarrow y) rightarrow ((x^n rightarrow 0) rightarrow y) rightarrow y) approx 1,,{rm for,some},n > 0. |
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