A new submodule clustering method via sparse and lowrank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic structures, e.g., image data kept as matrices. To implement clustering, the multi-way data, viewed as tensors, are represented by the proposed tensor sparse an...

The algebras of the title are infinite-dimensional graded Lie L=?i=1?Li, over a field positive characteristic p, which generated by an element degree 1 and satisfy [Li,L1]=Li+1 for i?p. In case p=2 such were classified Caranti Vaughan-Lee in 2003. We announce extension that classification to arbitrary prime characteristic, prove several major steps its proof.

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

We consider a local (or standard graded) ring R R with ideals alttext="script upper I prime"> <mml:mrow class="MJX-TeXAtom-O...

We study the generic tropical initial ideals of a positively graded Cohen-Macaulay algebra R over an algebraically closed field k. Building on work Römer and Schmitz, we give formula for each ideal, express associated quasivaluations in terms certain I-adic filtrations. As corollary, show that case is domain, every ideal coming from codimension 1 skeleton variety prime, so “generic presentation...

The notion of intuitinitic (T, S)-fuzzy submodule in Module is introduced, and related properties are investigated. Mathematics Subject Classification: 08A72, 13C99

We investigate deformations of skew group algebras arising from the action symmetric on polynomial rings over fields arbitrary characteristic. Over real or complex numbers, Lusztig’s graded affine Hecke algebra and analogs are all isomorphic to Drinfeld algebras, which include symplectic reflection rational Cherednik algebras. prime characteristic, new arise that capture both a disruption also ...