國立虎尾科技大學 |

The Characterization of Finite Elasticities = Factorization Theory in Krull Monoids via Convex Geometry /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Characterization of Finite Elasticities/ by David J. Grynkiewicz.
其他題名:	Factorization Theory in Krull Monoids via Convex Geometry /
作者:	Grynkiewicz, David J.
面頁冊數:	XII, 282 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Convex and Discrete Geometry. -
電子資源:	https://doi.org/10.1007/978-3-031-14869-9
ISBN:	9783031148699

The Characterization of Finite Elasticities = Factorization Theory in Krull Monoids via Convex Geometry /
Grynkiewicz, David J.

The Characterization of Finite ElasticitiesFactorization Theory in Krull Monoids via Convex Geometry /[electronic resource] :by David J. Grynkiewicz. - 1st ed. 2022. - XII, 282 p. 1 illus.online resource. - Lecture Notes in Mathematics,23161617-9692 ;. - Lecture Notes in Mathematics,2144.

This book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory’s Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra) This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.

ISBN: 9783031148699

Standard No.: 10.1007/978-3-031-14869-9doiSubjects--Topical Terms:

672138
Convex and Discrete Geometry.

LC Class. No.: QA241-247.5

Dewey Class. No.: 512.7

The Characterization of Finite Elasticities = Factorization Theory in Krull Monoids via Convex Geometry /
LDR:02641nam a22003975i 4500 001 1084769
003 DE-He213
005 20221026032354.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031148699 $9 978-3-031-14869-9
024 7 $a 10.1007/978-3-031-14869-9 $2 doi
035 $a 978-3-031-14869-9
050 4 $a QA241-247.5
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.7 $2 23
100 1 $a Grynkiewicz, David J. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1076683
245 1 4 $a The Characterization of Finite Elasticities $h [electronic resource] : $b Factorization Theory in Krull Monoids via Convex Geometry / $c by David J. Grynkiewicz.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XII, 282 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Lecture Notes in Mathematics, $x 1617-9692 ; $v 2316
520 $a This book develops a new theory in convex geometry, generalizing positive bases and related to Carathéordory’s Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra) This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization. While factorization into irreducibles, called atoms, generally fails to be unique, there are various measures of how badly this can fail. Among the most important is the elasticity, which measures the ratio between the maximum and minimum number of atoms in any factorization. Having finite elasticity is a key indicator that factorization, while not unique, is not completely wild. Via the developed material in convex geometry, we characterize when finite elasticity holds for any Krull domain with finitely generated class group $G$, with the results extending more generally to transfer Krull monoids. This book is aimed at researchers in the field but is written to also be accessible for graduate students and general mathematicians.
650 2 4 $a Convex and Discrete Geometry. $3 672138
650 2 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 1 4 $a Number Theory. $3 672023
650 0 $a Discrete geometry. $3 672137
650 0 $a Convex geometry . $3 1255327
650 0 $a Group theory. $3 527791
650 0 $a Commutative rings. $3 672474
650 0 $a Commutative algebra. $3 672047
650 0 $a Number theory. $3 527883
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031148682
776 0 8 $i Printed edition: $z 9783031148705
830 0 $a Lecture Notes in Mathematics, $x 0075-8434 ; $v 2144 $3 1254300
856 4 0 $u https://doi.org/10.1007/978-3-031-14869-9
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-LNM
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)