On the second and weakly-second spectrum of a module
Speaker
Marta Maloid-Glebova
Department of Algebra, Topology and Fundamental Mathematics
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv
When & where:
November 30, 2021 at 1500,
online Zoom
Join Zoom Meeting:
https://us04web.zoom.us/j/739…
Meeting ID: 739 806 9872
Passcode: AUpYx5
Abstract of talk
In this talk, we study second modules over associative rings and give some basic properties of this concept. Also we define the notion of weakly-second submodule of a module over an arbitrary ring and study some relationships between second spectrum and weakly-second spectrum of a module.
November 30, 2021
be a associative ring and 
an multiplicative 
be the the collection of all second submodules of 
is carried out. Some results obtained by using the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group 
are presented.
is the 
– dimensional Minkowski space; 
is the real number axis of the dependent variable 
.
in a homomorphic image of a commutative Bezout domain of stable range 1.5 is developed. It is proved that the set of solutions of a solvable linear equation contains at least one solution that divides the rest, which is called a generating solution. Generating solutions are pairwise associates. Using this result, the structure of elements of the Zelisko group is investigated.