The complement operation on modules has not been argued so far as we know. We observe that it plays an important role in software maintenance, as well as join and meet operations. A de nition of a module and operations on them is given in category theoretic terms; we adopt well-known characterization of complement as a left adjoint to join. The de nition is rst given locally and then extended t...

A new Gray map between codes over F2 +uF2 +uF2 +uF2 + ....+ uF2 and codes over F2 is defined. It is proved that the Gray image of a linear (1− um)-cyclic code over F2 + uF2 + uF2 + uF2 + .... + uF2 of length n is a binary distance invariant quasi-cylic code of index 2m−1 and length 2mn. It is also proved that if n is odd, then every code of length 2mn over F2 which is the Gray image of a linear...

The blob algebra is a finite-dimensional quotient of the Hecke type B which almost always quasi-hereditary. We construct indecomposable tilting modules for over field characteristic 0 in doubly critical case. Every module maximal highest weight either projective or an extension simple by module. Moreover, every submodule weight. conclude that graded Weyl filtration multiplicities this case are ...

This paper addresses the problem of designing a submodule of a given system ofcommunicating I/O automata. The problem may be formulated mathematically by theequation (C||X)rA under the constraint IX=In, where C represents the specification of theknown part of the system, called the context, A represents the specification of the whole system,X represents the specification of the ...