zero multiplication
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2020 ◽  
Vol 27 (03) ◽  
pp. 433-446 ◽  
Author(s):  
Matej Mencinger ◽  
Borut Zalar

We study complex involutive algebras generated by a single nonselfadjoint idempotent and use them to construct a family of algebras, which we call planar Lyapunov algebras. As our main result, we prove that every 2-dimensional commutative real algebra whose homogeneous Riccati differential equation is stable at the origin must be isomorphic either to an algebra with zero multiplication or to some planar Lyapunov algebra.


2018 ◽  
Vol 28 (08) ◽  
pp. 1565-1573 ◽  
Author(s):  
Ilya Ivanov-Pogodaev ◽  
Sergey Malev ◽  
Olga Sapir

This work provides an example of a finitely presented semigroup [Formula: see text] with zero containing an infinite ideal of the form [Formula: see text], where [Formula: see text] is a generator of [Formula: see text], such that every word in generators representing an element of [Formula: see text] is square free (i.e. any word of the type [Formula: see text], for non-empty [Formula: see text], equals zero in [Formula: see text]).


2014 ◽  
Vol 13 (04) ◽  
pp. 1350127
Author(s):  
CZESŁAW BAGIŃSKI ◽  
JÁNOS KURDICS

Let G be a finite nonabelian p-group and F a field of characteristic p and let [Formula: see text] be the subalgebra spanned by class sums [Formula: see text], where C runs over all conjugacy classes of noncentral elements of G. We show that all finite p-groups are subgroups and homomorphic images of p-groups for which [Formula: see text]. We also give the description of abelian-by-cyclic groups for which [Formula: see text] is an algebra with zero multiplication or is nil of index 2.


2001 ◽  
Vol 38 (1-4) ◽  
pp. 331-337
Author(s):  
R. Mlitz ◽  
R. Wiegandt

Beside near-rings with zero-multiplication or constant multiplication also other near- rings can be considered as near-rings with trivial multiplication. From a structure theoret- ical point of view it is reasonable to consider Kurosh{Amitsur radical classes which contain all near-rings with trivial multiplication. In the present note, continuing the investigations of [2], [4] and [5], we shall characterize the semisimple classes of such radical classes. Our characterizations look clumsier than those in [2], [4] and [5], but we exhibit that exact analogues of the mentioned characterizations cannot be achieved.


2000 ◽  
Vol 65 (3) ◽  
pp. 1115-1132 ◽  
Author(s):  
Oleg Belegradek ◽  
Ya'acov Peterzil ◽  
Frank Wagner

AbstractA structure (M, <, …) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1.


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