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Extending Structures for Gel’fand-Dorfman Bialgebras
Gel’fand-Dorfman bialgebra, which is both a Lie algebra and a Novikov algebra with some compatibility condition, appeared in the study of Hamiltonian...
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Classifying Recollements of Derived Module Categories for Derived Discrete Algebras
We study a class of derived discrete Nakayama algebras. All indecomposable compact objects in the derived module category are determined and all...
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The theory of screws derived from a module over the dual numbers
The theory of screws clarifies many analogies between apparently unrelated notions in mechanics, including the duality between forces and angular...
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On a Generalization of FI-Extending Modules
In this paper, we introduce modules with the property that every f-closed submodule has a complement which is a direct summand. We provide some...
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The module theory of semisymmetric quasigroups, totally symmetric quasigroups, and triple systems
This paper initiates a unified module theory for four varieties of quasigroups: semisymmetric, semisymmetric idempotent, totally symmetric, and...
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Hilbert C∗-Module for Analyzing Structured Data
Generalizing data analysis in Hilbert spaces to Hilbert C∗-modules has been investigated. This generalization enables us to analyze structured data...
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Extending Network Tools to Explore Trends in Temporal Granular Trade Networks
Bilateral trade relationships have been under increased scrutiny by the economic literature for their relevant role in influencing economic growth...
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Bilinear forms in the Jacobian module and binding of N-spectral chains of a hypersurface with an isolated singularity
Using his deep and beautiful idea of cutting with a Hyperplane, Lefschetz explained how the homology groups of a projective smooth variety could be...
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Relative Weak Injective and Weak Flat Modules with Respect to a Semidualizing Module
Let R be a commutative ring, and let C be a semidualizing R -module. We introduce the notion of finitely presented C -injective modules, finitely...
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On extending Ck functions from an open set to ℝ with applications
For k ∈ ℕ ∪ {∞} and U open in ℝ, let C k ( U ) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f ...
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Extending Orders on Rings with Idempotents and d-elements
We investigate situations in which compatible orders on rings with idempotent elements can be extended to more restrictive orders without assuming...
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Betti numbers of the conormal module of licci rings
We establish lower bounds for the Betti numbers of the conormal module for licci ideals in a regular local ring. In particular, for a licci...
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Organising the module category
We describe here the work developed with my students along the years in the IME-USP.
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Projection Invariant t-Baer and Related Modules
We study the concepts of projection invariant t -extending modules and projection invariant t -Baer modules, which are generalized to the notions of...
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Exponentially Bounded C-semigroup and the Cauchy Initial Value Problems in Complete Random Normed Modules
In this paper, the notion of C -semigroup of continuous module homomorphisms on a complete random normal (RN) module is introduced and investigated....
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Dualizable and semi-flat objects in abstract module categories
In this paper, we define what it means for an object in an abstract module category to be dualizable and we give a homological description of the...
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On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules
We prove new results on the interplay between reduction numbers and the Castelnuovo–Mumford regularity of blowup algebras and blowup modules, the key...
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Decentralized distributed parameter tuning model to generate unidirectional movements
This study proposes a module designed for the automatic parameter control of peristaltic locomotion systems. The module comprises two populations of...
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Topological amenability and Köthe co-echelon algebras
We introduce a notion of a topologically flat locally convex module, which extends the notion of a flat Banach module and which is well adapted to...
