BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Alberto Facchini (University of Padua\, Italy)
DTSTART:20230814T150000Z
DTEND:20230814T160000Z
DTSTAMP:20260423T021123Z
UID:ENAAS/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/29/">H
 eaps and trusses</a>\nby Alberto Facchini (University of Padua\, Italy) as
  part of European Non-Associative Algebra Seminar\n\n\nAbstract\nI will pr
 esent the first notions concerning heaps and trusses. Heaps were introduce
 d for the first time by H. Prüfer (1924) and R. Baer (1929). A heap is a
  pair $(H\, [−\,−\,−])$ consisting of a set $H$ and a ternary operat
 ion $$[−\,−\,−] : H \\times H \\times H \\to H\, (x\, y\, z)  \\to
  [x\, y\, z]\,$$ such that\, for all $v\, w\, x\, y\, z \\in H\,$  \n$$[v\
 , w\, [x\, y\, z]] = [[v\, w\, x\, ]\, y\, z]\, \\ [x\, x\, y] = y\,\\ [y\
 , x\, x]= y.$$\n Truss is a much more recent algebraic structure (T. Brzez
 iński\,  2019). A truss is a heap with a further associative binary opera
 tion\, denoted by juxtaposition\, which distributes over $[−\,−\,−]\
 ,$ that is\, for all $w\, x\, y\, z \\in T\,$ \n$$w[x\, y\, z] = [wx\, wy\
 , wz]\, \\ [x\, y\, z]w = [xw\, yw\, zw]\,\\ [x\, y\, z] =[z\, y\, x].$$\n
LOCATION:https://researchseminars.org/talk/ENAAS/29/
END:VEVENT
END:VCALENDAR