image text special

‘Mirrored Latin’ by Jibril Esposito at PERBENTOTHAL

Sometimes, mirrored Latin symbols are used in Arabic mathematical notation


In mathematics, and in particular universal algebra, the concept of n-ary group (also called n-group or multiary group) is a generalization of the concept of group to a set G with an n-ary operation instead of a binary operation. By an n-ary operation is meant any set map from the n-th Cartesian power of G to G. The axioms for an n-ary group are defined in such a way that they reduce to those of a group in the case n=2.

The easiest axiom to generalize is the associative law. Ternary associativity is the polynomial identity (abc). The equality of the three possible bracketings of the string abcde in which any three consecutive symbols are bracketed. (Here it is understood that the equations hold for arbitrary choices of elements a,b,c,d,e in G.) In general, n-ary associativity is the equality of the n possible bracketings of a string consisting of n+(n-1) = 2n-1 distinct symbols with any n consecutive symbols bracketed. A set G which is closed under an associative n-ary operation is called an n-ary semigroup. A set G which is closed under any (not necessarily associative) n-ary operation is called an n-ary groupoid.

The inverse axiom is generalized as follows: in the case of binary operations the existence of an inverse means ax = b has a unique solution for x, and likewise xa = b has a unique solution. In the ternary case we generalize this to abx = c, axb = c and xab = c each having unique solutions, and the n-ary case follows a similar pattern of existence of unique solutions and we get an n-ary quasigroup.

An n-ary group is an n-ary semigroup which is also an n-ary quasigroup.

'Her Own Devices' by Laurie Kang at Franz Kaka, Toronto

'THE MOUTH OF THE GIFTED HORSE' by Wisrah Villefort at Goswell Road, Paris

'FRESH' by Rune Bering and Kevin Josias at Tableau, Copenhagen

Armen Avanessian: ‘So let us ask, why we still call this a capitalist world?’

'Dream again of better Generationenvertrag' by Niklas Taleb at Lucas Hirsch, Duss

'TOYS' by Jascha Schieche at FONDA, Leipzig

'YOU ARE HERE' by Linda Lerseth at Podium, Oslo

'Space Almond Head Void' by Sasha Auerbakh at GOMO, Vienna

'UwU' by Tea Strazicic at ung5, Cologne

'Friends Objects' by Helin Alas at Loggia, Munich

'Talent Didn’t Bring Me Here' by Günther Möbius at BPA Space, Cologne

'P**** B**** ARENA' by Isabelle Frances McGuire at Good Weather (Hosted by Et al.

'Flat Tire' by Janis Dzirnieks at Robert Fruinstraat 56, Rotterdam

'Sheets of Past and Layers of Reality', a Group Show at Hoib, Tallinn

Garden Cult Triennale, Chapter I: Sopot, Poland

'踢館 Tek Kwun' at Tai Kwun Centre for Heritage and Arts, Hong Kong

'Theological Time, Mean Landscape, Circumcision Throne, Burping Bird, Auto-censur

'More than two eyes' by Eliška Konečná and Michael Nosek at Berlinskej Model, Pra

Next Page