On The Generalization Of The Greatest Common Divisor Matrices

The thesis is a research on the GCD matrix on the direct product of some finite sets of positive integers.by means of moebius inversion and the theory of tensor product ,We study the structure and the bounds for the determinants of GCD matrices on the direct product.We obtain some results to be similar to the GCD matrix on the finite sets of positive integers.Finally,we genralize the results to the direct product of general partially ordered sets .the thesis consists of two parts :In the first part, we study the GCD matrix on the direct product of some finite sets of postive integers.We get the meet matrix is positive definite and have the upper and lower bounds for the detminants of GCD matrices.In the second part, we study the structure and the detminant's bounds of meet matrix on the direct product of general partially ordered sets .We obtain some results to be similar to the first part.