Semigroups and S-polygons with annihilation conditions


Yuriy Ishchuk

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of Lviv

November 21, 2017 at 15:05 in Lecture Room 377

Abstract of talk

The notions of a semi-commutative semigroup and an abelian S-polygon can be introduced by analogy with the notions of semi-commutative, abelian modules and rings.

A semigroup S is called a semi-commutative semigroup if for any x,y\in S, xy=0 implies xSy=0. A right S-polygon A_S is called abelian if for any a\in A_S and any s\in S, any idempotent e\in S, ase = aes. Using the notions of Baer’s conditions for modules I will introduce p.p.-Baer S-polygons and prove that if A_S is a p.p.-Baer S-polygon, then the conditions for A_S to be a reduced, symmetric, semicommutative and an abelian S-polygon are equivalent.

Yuriy Ishchuk
November 21, 2017