We study representations of nilpotent type nontrivial liftings of quantum linear spaces and their Drinfel’d quantum doubles. We construct a family of Vermatype modules in both cases and prove a parametrization theorem for simple modules. We compute the Loewy and socle series of Verma modules under a mild restriction on the datum of a lifting. We find bases and dimensions of simple modules.

We study representations of nilpotent type nontrivial liftings of quantum linear spaces and their Drinfel’d quantum doubles. We construct a family of Vermatype modules in both cases and prove a parametrization theorem for the simple modules. We compute the Loewy and socle series of Verma modules under a mild restriction on the datum of a lifting. We find bases and dimensions of simple modules.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

Let $R$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎Let $M$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎Then $M$ has a direct decomposition $M=oplus_{iin I} M_i$‎,‎where each $M_i$ is noetherian quasi-projective and each‎‎endomorphism ring $End(M_i)$ is local‎.

A. F. Mulla, Dr.R. S. Patil [email protected] Abstract Digital images play an important role both in daily life applications as well as in areas of research and technology. Due to the increasing traffic caused by multimedia information and digitized form of representation of images; image compression has become a necessity. Wavelet transform has demonstrated excellent image compression perf...