Abstract
The paper reviews the author’s results in the theory of elementary nets (carpets). In particular, closed (admissible) nets are investigated. For an elementary net (a net considered without the diagonal) of additive subgroups of an arbitrary commutative ring, the concepts of the derivative net, the closure of the net, and the net associated with the elementary group are introduced. Factorization of the elementary groups is proposed. This factorization is then used to construct an example of a closed (admissible) net which cannot be completed to a (complete) net. For a third-order elementary net σ of additive subgroups of a commutative ring, decomposition of an elementary transvection from the elementary group E(σ) is obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
