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Abstract: For a commutative noetherian ring R, we investigate relations between tilting and cotilting modules in and , where runs over the maximal spectrum of R. For each , we construct a correspondence between (equivalence classes of) n-cotilting R-modules C and (equivalence classes of) compatible families of n-cotilting -modules ( ). It is induced by the assignment , where is the colocalization of C at , and its inverse . We construct a similar correspondence for n-tilting modules using compatible families of localizations; however, there is no explicit formula for the inverse. [Copyright &y& Elsevier]

In this work, we present a number of generator matrices of the form [ I 2 n | τ 2 (v) ] , where I 2 n is the 2 n × 2 n identity matrix, v is an element in the group matrix ring M 2 (R) G and where R is a finite commutative Frobenius ring and G is a finite group of order 18. We employ these generator matrices and search for binary [ 72 , 36 , 12 ] self-dual codes directly over the finite field F 2. As a result, we find 134 Type I and 1 Type II codes of this length, with parameters in their weight enumerators that were not known in the literature before. We tabulate all of our findings. [ABSTRACT FROM AUTHOR]