Higher degree forms are homogeneous polynomials of d>2, or equivalently symmetric d-linear spaces. This paper is mainly concerned about the algebraic structure centres higher with applications specifically to direct sum decompositions, namely expressing as sums in disjoint sets variables. We show that centre algebra almost every form ground field, consequently all absolutely indecomposable. If ...

In a recent pair of contributions [2, 3], starting from a set of results about the relationship between the direct sum decomposition of (linear, time-invariant, differential) behaviors and the solvability of certain two-sided Bézout equations, it was shown that every autonomous behavior can be expressed as a direct sum of irreducible components. In this contribution, we further explore this iss...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

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 module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...