Let p ≥ 3 be a prime. We consider the cyclotomic extension Z(p)[ζp2] of Z(p), with Galois group G := (Z/p2)∗. Since this extension is wildly ramified, Z(p)[ζp2] is not projective as a module over the group ring Z(p)G (Speiser). Extending this module structure, we can regard Z(p)[ζp2 ] as a module over the twisted group ring Z(p)[ζp2] ≀G; as such, it remains faithful and non projective. We calcu...

The ML module system enables flexible development of large software systems by its support of nested structures, functors and signatures. In spite of this flexibility, however, recursion between modules is prohibited, since dependencies between modules must accord with the order of definitions. As a result of this constraint, programmers may have to consolidate conceptually separate components ...

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

Let $(R,\mathfrak{m},\mathbb{k})$ be an equicharacteristic one-dimensional complete local domain over algebraically closed field $\mathbb{k}$ of characteristic 0. R. Berger conjectured that R is regular if and only the universally finite module differentials $\Omega_R$ a torsion-free $R$-module. We give new cases this conjecture by extending works G\"uttes (Arch Math 54:499-510, 1990) Corti\~na...

Extending ideas of Hedden-Ni, we show that the module structure on Khovanov homology detects split links. We also prove an analogue for untwisted Heegaard Floer branched double cover. Technical results proved along way include two interpretations in terms twisted and fact reduced complex a link is well defined up to quasi-isomorphism.

Programmable Metamaterials The study of the ancient paper art kirigami based materials mainly focuses on form 2D thin sheets. In article number 2105641, Jie Yin and co-workers report extending conventional to 3D modular construct programmable architected materials. module can transform into versatile configurations their conformable assembly creates multidimensional disassembalable metamaterial...

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.