An answer to Demircis open question, a clarification of his result, and a correction of his interpretation of the result

In his note (this issue of this journal), Demirci shows that fields with fuzzy equalities have only trivial fuzzy equalities, concludes that "Therefore, in case L-algebras contain field structure, all results in [R. Belohlavek, Fuzzy Relational Systems: Foundations and Principles, Kluwer Academic\Plenum Publishers, New York, 2002; R. Belohlavek, V. Vychodil, Algebras with fuzzy equalities, in: proceedings of the 10th IFSA world congress, June 29–July 2, 2003, pp. 1–4; R. Belohlavek, V. Vychodil, Algebras with fuzzy equalities, Fuzzy Sets and Systems, accepted; V. Vychodil, Direct limits and reduced products of algebras with fuzzy eqalities, submitted] are evident from their classical counterparts", and asks a question "does there exist any L-algebra with an L-equality different from trivial L-equalities in case the ordinary part of the L-algebra includes two binary operations that define group, ring, module or vector space structure?" In our reply, we show the following. First, by presenting examples of group-based L-algebras with non-trivial L-equalities, we show that the answer to Demirciʹs question is positive. Second, we clarify the meaning of Demirciʹs result and show that it is in fact a natural generalization of the well-known classical result saying that ordinary fields do not have non-trivial congruences. Third, we argue that Demirciʹs interpretation of his result is mistaken and that it is not true that "all results in [R. B?lohl?vek, Fuzzy Relational Systems: Foundations and Principles, Kluwer Academic\Plenum Publishers, New York, 2002; R. Belohlavek, V. Vychodil, Algebras with fuzzy equalities, Fuzzy Sets and Systems, to appear; R. Belohlavek, V. Vychodil, Fuzzy Equational Logic, Springer, Berlin, to appear; S. Burris, H.P. Sankappanavar, A Course in Universal Algebra, Springer, New York, 1981] are evident from their classical counterparts."