Abstract
where ix, x j, xij~X. The elements xx . . . . . x, will be called the elements in the outer row, ix,. . . . . x in the outer column and all the remaining elements the inner elements of the table. Since the inner elements form a n • n-matrix we shall speak about its rows and columns as about the inner rows and the inner columns. Two tables will be called equivalent if they belong to the same monoid, two tables will be called weakly equivalent if they belong to the isomorphic monoids. Omitting some elements in the multiplication table we get a partial table of a monoid. Our main concern will be with the question, how many elements we can omitt in the table under the condition that the monoid could be uniquely reconstructed from the partial table. Having a set X we can construct a partial table over X. By it we mean a rectangular scheme of the type (1) when some of the elements may be omitted. We see three questions connected with partial tables over X.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.