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Combinatorics of involutive divisions [article]

Michela Ceria
2017 arXiv   pre-print
In order to deal with this problem, we introduce two graphs as tools, one is strictly related to Seiler's L-graph, whereas the second generalizes it, to cover the case of "non-continuous" (in the sense  ...  Indeed, given an element in the ideal (resp. escalier), walking backwards (resp. forward) in the graph, we can identify all the other generators of the ideal (resp. elements of degree D in the escalier  ...  : 1. there are no oriented paths from t to s; lcm(s, t) ∈ C L (t, U) We call such a graph a generalized Ufnarovsky-like graph.  ... 
arXiv:1707.02452v1 fatcat:a24sakuvdzcxfbwyhnww6bc7ei

On the Calculation of gl.dimG^N(A) and gl.dimA by Using Gröbner Bases [article]

Huishi Li
2008 arXiv   pre-print
It is shown how to use the Ufnarovski graph Γ ( LM( G)) and the graph of n-chains Γ_ C( LM( G)) to calculate gl.dimG^N(A) and gl.dimA, where G^N(A), respectively A, is the associated N-graded algebra of  ...  Let A=K< X_1,...,X_n> /< G> be a K-algebra defined by a finite Gröbner basis G.  ...  Then the Ufnarovski graph of Ω (introduced by V.  ... 
arXiv:0805.0686v1 fatcat:cf5en46drbamhl3qbrxifopvea


2011 International journal of algebra and computation  
of primitive words that label loops of the Ufnarovsky graph of the presentation. [25] J.  ...  Wolf, "Growth of finitely generated solvable groups and curvature of Riemannian manifolds", J. Differential Geom. 2 (1968), 421-446.  ...  1) for some primitive word z that labels a loop of the Ufnarovsky graph.  ... 
doi:10.1142/s0218196711006182 fatcat:y2juryf73jdofcrc226xutgsom

Page 6017 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
by computer algebra (217-223); Peter Schenzel, On curves of small degree on a nor- mal rational surface scroll (225-239); Anna Torstensson, Victor Ufnarovski [V.  ...  Dobbs, Marco Fontana and Gabriel Picavet, Generalized going-down homomorphisms of commutative rings (143-163); Said El Baghdadi, The class group of the composite ring of a pair of Krull domains and applications  ... 

Entropy of monomial algebras and derived categories [article]

Li Lu, Dmitri Piontkovski
2021 arXiv   pre-print
Moreover, we relate these two kinds of entropy with the topological entropy of the Ufnarovski graph of A and the entropy of the path algebra of the graph.  ...  Let A be a finitely presented associative monomial algebra. We study the category qgr(A) which is a quotient of the category of graded finitely presented A-modules by the finite-dimensional ones.  ...  Moreover, h(L) is equal to the topological entropy h(Q A ) of the Ufnarovski graph Q A of A.  ... 
arXiv:2103.03946v1 fatcat:7xlh7vrmdjax5bui3t53566334

Regular Gröbner Bases

Jonas MÅnsson, Patrik Nordbeck
2002 Journal of symbolic computation  
In this paper we introduce the concept of bi-automaton algebras, generalizing the automaton algebras previously defined by Ufnarovski.  ...  A bi-automaton algebra is a quotient of the free algebra, defined by a binomial ideal admitting a Gröbner basis which can be encoded as a regular set; we call such a Gröbner basis regular.  ...  According to the proof of Theorem 9(d) in Ufnarovski (1989) , the finite union G = ∪ x,y∈P {xwy − yxw | w ∈ c * y } is a Gröbner basis for the ideal generated by the present commutators.  ... 
doi:10.1006/jsco.2001.0500 fatcat:saohwxqd6re6lnvbjhtr2l7dbm

Page 2065 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
Victor A. Ufnarovski (Lund) 96d:13043 13P10 Ramella, Isabella (I- NAPL-AM; Naples) Ideals of points in generic position: a polynomial algorithm for computing a minimal set of generators.  ...  Alessandro Logar (Trieste) 96d:13042 13P10 0SC15 de Loera, Jestis A. (1-CRNL-AM; Ithaca, NY) Grébner bases and graph colorings. (English summary) Beitrége Algebra Geom. 36 (1995), no. 1, 89-96.  ... 

Page 2540 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
Lopez-Permouth, A survey on the theory of weakly-injective modules (205-232); Todd C. Torgersen, Distributing symbolic computations on a net- work of workstations (233-246); V. A. Ufnarovski [V. A.  ...  Summary: “Let A = M — N be a regular splitting of an M-matrix. We give some equivalent properties which are equivalent to graph compatible splittings.  ... 

Page 497 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
Green], Teo Mora and Victor Ufnarovski [V. A. Uf- narovskii], The non-commutative Grébner freaks (93-104); Ben- jamin J.  ...  Akl, Spanning subgraphs with applications to communi- cation on a subclass of the Cayley-graph-based networks (79-96); Luisa Gargano, Adele A.  ... 

Non-commutative computer algebra and molecular computing

Svetlana Cojocaru, Victor Ufnarovski
2001 Computer Science Journal of Moldova  
The main idea is that one can get more advantage in using molecular computing for non-commutative computer algebra compared with a commutative one.  ...  But what is more important that a free subgroup with a larger number of generators (even infinitely many) is simply a subgroup of our 2-generated group.  ...  Among them the most popular are the algorithms for the different graphs problems, SAT problem, the data encryption breaking etc.  ... 
doaj:0b760cb230f64ca6bbb2ba8f45516165 fatcat:eq64fnnxfzd5fpx7hcazk62jcy

Page 111 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
More precisely, given a non-oriented, loop-free graph A C X x X, the associated algebra R(X4) = (Llc R(x))/(ab — ba| a € R(x), b € R(y), (x,y) € A) is considered.  ...  Let A be an algebra generated by the finite alphabet X. Let w be a word in this alphabet that is maximal in the lexicographical ordering in the set of words that correspond to nonzero elements in A.  ... 

BERGMAN under MS-DOS and Anick's resolution

S. Cojocaru, V. Ufnarovski
1997 Discrete Mathematics & Theoretical Computer Science  
A table is provided permitting a comparison of the effectiveness of the calculations in BERGMAN with the other systems.  ...  International audience Noncommutative algebras, defined by the generators and relations, are considered.  ...  Let us consider a graph =(V;E); where the set of vertex consists of the union of the unit 1; alphabet X and all proper suffixes of the obstructions.  ... 
doi:10.46298/dmtcs.237 fatcat:j4pbe2adj5fdtb44xyyhdxw6fa

Page 3053 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
To any undirected graph A, Gel/fand and Ponomarev introduced a preprojective algebra P(A); it is finite-dimensional over a field K if and only if A is a disjoint union of Dynkin diagrams.  ...  [Cojocaru, Svetlana] (MO-AOS; Chisinau) ; Ufnarovski, V. [Ufnarovskii, V. A.] (MO-AOS; Chisinau BERGMAN under MS-DOS and Anick’s resolution. (English summary) Lie computations (Marseille, 1994).  ... 

Algebras and their Associated Monomial Algebras [article]

Huishi Li
2006 arXiv   pre-print
) is the associated Γ-graded K-algebra of A defined by FA, and < HT(I)> is the Γ-graded ideal of R generated by the set of head terms of I.  ...  Considering the Γ-grading filtration FR of R and the Γ-filtration FA induced by FR for the quotient K-algebra A=R/I, we show that there is a Γ-graded K-algebra isomorphism G(A)=R/< HT (I)>, where G(A  ...  Realization via Gröbner Bases and Ufnarovski Graphs Convention throughout the paper Let K be a field.  ... 
arXiv:math/0609583v1 fatcat:msj2ksc5ljaxzntfsnxe7q424u

Noetherianity and Ext

E.L. Green, N. Snashall, Ø. Solberg, D. Zacharia
2008 Journal of Pure and Applied Algebra  
Let R = R 0 ⊕ R 1 ⊕ R 2 ⊕ · · · be a graded algebra over a field K such that R 0 is a finite product of copies of K and each R i is finite dimensional over K .  ...  We pay particular attention to the case when R is a Koszul algebra and S is the Koszul dual to R.  ...  Moreover, since R is a Koszul algebra and S has the same quiver as R and relations generated by all the paths of length 2 not in ρ, we see that the relation graph of S is, in fact, the Ufnarovski graph  ... 
doi:10.1016/j.jpaa.2007.10.011 fatcat:k6r6gitxm5bexjgkl3qagbm3wu
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