Let A d be the complex polynomial ring in d variables. A contractive A d-module is Hilbert space H equipped with an A d action such that for any ξ 1 , ξ 2 ,. Such objects have been shown to be useful for modeling d-tuples of mutually commuting operators acting on a Hilbert space. An example is given by H 2 d , which is the Hilbert space of holomorphic functions on B d = {z ∈ C d : |z| ≤ 1} gene...

There is much we still do not know about projective spaces. We describe here how the mod two cohomology of each real projective space is built as an unstable module over the Steenrod algebra A, or equivalently, over K, the algebra of inherently unstable mod two “lower operations” originally introduced by Steenrod. In particular, to produce the cohomology of projective space of each dimension we...

The Garsia–Haiman module is a bigraded Sn-module whose Frobenius image Macdonald polynomial. method of orbit harmonics promotes an Sn-set X to graded polynomial ring. can be applied prove cyclic sieving phenomena which notion that encapsulates the fixed-point structure finite group action on set. By applying this idea module, we provide results regarding enumeration matrices are invariant under...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

A navigation system for an autonomous mobile robot working in indoor environments is presented. The system takes advantage of deliberative (plan-based) approach and reactive (behavior-based) approach. In the reactive part of the system are local behaviors that are independent, action-generating entities. We also provide higher-level deliberative modules that make interactions manageable so the ...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

An R-module M is called epi-retractable if every submodule of MR is a homomorphic image of M. It is shown that if R is a right perfect ring, then every projective slightly compressible module MR is epi-retractable. If R is a Noetherian ring, then every epi-retractable right R-module has direct sum of uniform submodules. If endomorphism ring of a module MR is von-Neumann regular, then M is semi-...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...