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Gluing semigroups and strongly indispensable free resolutions

Mesut Şahi̇n, Leah Gold Stella
2019 International journal of algebra and computation  
We give a naive condition to determine whether gluing of two semigroup rings has a strongly indispensable minimal free resolution.  ...  of any embedding dimension, having strongly indispensable minimal free resolutions.  ...  Gluing Strongly Indispensable Resolutions Let S 1 = N{a 1 , . . . , a m } and S 2 = N{b 1 , . . . , b n } be two affine semigroups.  ... 
doi:10.1142/s0218196719500012 fatcat:nzdgqdiumne4pggl55s4cwvbuq

On the generalized Scarf complex of lattice ideals [article]

Hara Charalambous, Apostolos Thoma
2009 arXiv   pre-print
We present the generalized Scarf complex of I_Ł and show that it is indispensable in the sense that it is contained in every minimal free resolution of R/I_Ł.  ...  Let k be a field, L⊂Z^n be a lattice such that Ł∩N^n={ 0}, and I_Ł⊂[x_1,..., x_n] the corresponding lattice ideal.  ...  As a final note we remark that it is easy to produce examples where the three complexes are different, by combining the two previous examples and using the technique of gluing semigroups, see [22] .  ... 
arXiv:0901.1208v1 fatcat:rmvaozad2jginhj5ri4cvxpdfm

On the generalized Scarf complex of lattice ideals

Hara Charalambous, Apostolos Thoma
2010 Journal of Algebra  
We present the generalized Scarf complex of I L and show that it is indispensable in the sense that it is contained in every minimal free resolution of R/I L .  ...  Suppose now that c / ∈ J 1 and c max( J 1 ). Therefore c = a, c < max( J ) and supp(x max( J )−c ) ∩ v-supp J ( J ) = ∅.  ...  As a final note we remark that it is easy to produce examples where the three complexes are different, by combining the two previous examples and using the technique of gluing semigroups, see [23] .  ... 
doi:10.1016/j.jalgebra.2009.12.019 fatcat:t4rgzmvay5f77ioalzzeginpmq

INTRODUCTION TO BASIC TORIC GEOMETRY

GOTTFRIED BARTHEL, LUDGER KAUP, KARL-HEINZ FIESELER
2007 Singularities in Geometry and Topology  
To every N -fan ∆, one associates the toric variety X ∆ := σ∈∆ X σ by gluing the family of affine toric varieties (X σ ) σ∈∆ , where X σ and X e σ are glued along the common open affine invariant subvariety  ...  only if N is a saturated sublattice (i.e., if N/N is torsion-free and thus, free: In that case, there is a one-sided inverse to ι that, upon tensoring with C * , provides a one-sided inverse on the level  ...  The theory of toric surface singularities and their resolution is particularly rich and fascinating.  ... 
doi:10.1142/9789812706812_0001 fatcat:5fi6oqie5jcj3mx7qr4vlzekea

Short Steps in Noncommutative Geometry [article]

Ahmad Zainy Al-Yasry
2019 arXiv   pre-print
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative  ...  Let S be a semigroup and let R be a commutative ring.  ...  They also find use in constructions such as Godement resolutions. 18.8. Ringed spaces and locally ringed spaces.  ... 
arXiv:1901.03640v1 fatcat:usxvglooabfg5hntp2ep2j2qtu

Bivariant K- and Cyclic Theories [chapter]

Joachim Cuntz
2005 Handbook of K-Theory  
For computations of KK and other K-theoretic invariants, the following long exact sequences associated to an extension are an indispensable tool.  ...  Given a C * -algebra A, let QA denote the free product A * A.  ... 
doi:10.1007/978-3-540-27855-9_14 fatcat:gsywm3ikibf7veft23dhao5jnq

Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality [article]

David Hansen
2014 arXiv   pre-print
on work of Ash-Stevens, Urban, and others.  ...  Using the overconvergent cohomology modules introduced by Ash and Stevens, we construct eigenvarieties associated with reductive groups and establish some basic geometric properties of these spaces, building  ...  When Γ(x i ) is torsion-free for each x i ∈ γ(K f ), we choose a finite resolution F • (x i ) → Z → 0 of Z by free left Z[Γ(x i )] -modules of finite rank as well as a homotopy equivalence F • (x i ) fi  ... 
arXiv:1412.1533v1 fatcat:573xwtnsfnafbfwtzce7fqv34q

Spectral Invariants of Operators of Dirac Type on Partitioned Manifolds [article]

David Bleecker, Bernhelm Booss-Bavnbek
2003 arXiv   pre-print
Moreover, we utilize the heat equation approach in various settings and show how these topological and spectral invariants are mutually related in the study of additivity and nonadditivity properties on  ...  the eta invariant of operators of Dirac type on closed manifolds and manifolds with boundary.  ...  We obtain the bundle E 1 by gluing two halves of D 2 × C by σ(ϕ) = e iϕ and E −1 by gluing with the adjoint symbol.  ... 
arXiv:math/0304214v1 fatcat:zc7fsk4oefhhfgr2j2jjlrwjwq

Update to "A Survey of Abstract Algebraic Logic"

J. M. Font, R. Jansana, D. Pigozzi
2009 Studia Logica: An International Journal for Symbolic Logic  
Acknowledgements The first and the second author have been supported by the Spanish grant BFM2001-3329 and the Catalonian grant 2001SGR-00017.  ...  The work of the third author is supported in part by the National Science Foundation under grants CCR-9803843 and CCR-0097907.  ...  in equality-free languages, such as the the existence of free structures and subdirect representation.  ... 
doi:10.1007/s11225-009-9169-2 fatcat:xunhvdtrifaanhbynrr23if7aa

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J. M. Font, R. Jansana, D. Pigozzi
2012 Studia Logica: An International Journal for Symbolic Logic  
Acknowledgements The first and the second author have been supported by the Spanish grant BFM2001-3329 and the Catalonian grant 2001SGR-00017.  ...  The work of the third author is supported in part by the National Science Foundation under grants CCR-9803843 and CCR-0097907.  ...  in equality-free languages, such as the the existence of free structures and subdirect representation.  ... 
doi:10.1023/a:1024621922509 fatcat:2siblipedbhkfihsps4cdcpmry

Asymptotic analysis of operator families and applications to resonant media [article]

Kirill D. Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev, Vladimir A. Ryzhov, Luis O. Silva
2022 arXiv   pre-print
Naboko and his students, and on the other hand, to concrete applications of current interest in the physics and engineering communities.  ...  We give an overview of operator-theoretic tools that have recently proved useful in the analysis of boundary-value and transmission problems for second-order partial differential equations, with a view  ...  and the study of spectral resolutions of identity.  ... 
arXiv:2204.01199v1 fatcat:iqih6kofcjh23kktsierizgwd4

New Approach to Arakelov Geometry [article]

Nikolai Durov (Max Planck Institute for Mathematics, St.Petersburg State University)
2007 arXiv   pre-print
This theory of generalized rings and schemes is developed up to construction of algebraic K-theory, intersection theory and Chern classes.  ...  In order to construct such an approach we develop a theory of generalized rings and schemes, which include classical rings and schemes together with "exotic" objects such as F_1 ("field with one element  ...  We can also consider the submonad W + ⊂ W given by W + (X) = W (X) if X = ∅, W + (∅) = ∅; this is also a monad without constants, and W + -Mod is the category of semigroups. 4.3.12.  ... 
arXiv:0704.2030v1 fatcat:au3axc3et5fstln7oa7gjb2z5i

Dagstuhl Reports, Volume 5, Issue 3, March 2015, Complete Issue [article]

2015
We aim at creating such a collection of argument sharing exemplars that will be a useful resource for linguistic analysis and grammar developing.  ...  For example, the restriction of a context-free graph language by a logical sentence is again context-free, and it can be decided whether all graphs/finitely many graphs/no graphs of a given context-free  ...  We consider some geometric queries that do not fit in the traditional semigroup searching/reporting model.  ... 
doi:10.4230/dagrep.5.3 fatcat:frrv4bul5rhfhh3jo4hv5l5uoi

TECHNOLOGICAL PROVIDING OF SURFACE LAYER PERFORMANCES OF PARTS DURING THE MACHINING

A.N. Sutyagin, A.N. Sutyagin
2020
Also paper presents operation of a newly-developed software providing visualization of topography of a machined surface on the basis of ISO 25000 standard and taking into account physical and mechanical  ...  The article describes the problem of friction unit surface layer parts wear resistance assurance based on control of geometrical and physic mechanical properties to be formed the machining.  ...  The spectral resolution of a spectrometer with a fiber optic probe is less than 3 nm, the spatial resolution when scanning the probe along the wound surface is about 1 mm.  ... 
doi:10.34660/inf.2020.19.79.001 fatcat:hpwjovfu5nf6zi2tuppahubyhe