caa a22 4500 467899649 CHVBK 20180406152814.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s00012-006-1994-9 doi (NATIONALLICENCE)springer-10.1007/s00012-006-1994-9 An implication basis for linear forms [Elektronische Daten] [R. Padmanabhan, P. Penner] Abstract.: The main results of this paper are a generalization of the results of S. Fajtlowicz and J. Mycielski on convex linear forms. We show that if Vn is the variety generated by all possible algebras $$ \user1{\mathcal{A}} = \left\langle {{\mathbf{R}};f} \right\rangle $$ , where R denotes the real numbers and $$ f(x_1 , \ldots x_n ) = p_1 x_1 + \cdots + p_n x_n $$ , for some $$ p_1 , \ldots p_n \in {\mathbf{R}} $$ , then any basis for the set of all identities satisfied by Vn is infinite. But on the other hand, the identities satisfied by Vn are a consequence of gL andμn, whereμn is the n-ary medial law and the inference rule gL is an implication patterned after the classical rigidity lemma of algebraic geometry. We also prove that the identities satisfied by $$ \user1{\mathcal{A}} = \left\langle {{\mathbf{R}};f} \right\rangle $$ are a consequence of gL andμn iff {p1, ... , pn} is algebraically independent. We then prove analagous results for algebras $$ \user1{\mathcal{A}} = \left\langle {{\mathbf{R}};f} \right\rangle $$ of arbitrary type τ and in the final section of this paper, we show that analagous results hold for Abelian group hyperidentities. Birkhäuser Verlag, Basel, 2007 linear forms nationallicence abelian groups nationallicence hyperidentities nationallicence term condition nationallicence rule (gL) nationallicence switching identities nationallicence Padmanabhan R. Department of Mathematics, University of Manitoba, Man. R3T 2N2, Winnipeg, Canada aut Penner P. Department of Mathematics, University of Manitoba, Man. R3T 2N2, Winnipeg, Canada aut algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/2-3(2006-08-01), 355-368 0002-5240 55:2-3<355 2006 55 12 https://doi.org/10.1007/s00012-006-1994-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00012-006-1994-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Padmanabhan R. Department of Mathematics, University of Manitoba, Man. R3T 2N2, Winnipeg, Canada aut NATIONALLICENCE 700 1- Penner P. Department of Mathematics, University of Manitoba, Man. R3T 2N2, Winnipeg, Canada aut NATIONALLICENCE 773 0- algebra universalis Birkhäuser-Verlag; www.birkhauser.ch 55/2-3(2006-08-01), 355-368 0002-5240 55:2-3<355 2006 55 12 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer