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Jespers E., Okninski J. — Noetherian Semigroup Algebras
Jespers E., Okninski J. — Noetherian Semigroup Algebras

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Название: Noetherian Semigroup Algebras

Авторы: Jespers E., Okninski J.

Аннотация:

Within the last decade, semigroup theoretical methods have occurred naturally in many aspects of ring theory, algebraic combinatorics, representation theory and their applications. In particular, motivated by noncommutative geometry and the theory of quantum groups, there is a growing interest in the class of semigroup algebras and their deformations.

This work presents a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have been recently intensively studied. Several concrete constructions are described in full detail, in particular intriguing classes of quadratic algebras and algebras related to group rings of polycyclic-by-finite groups. These give new classes of Noetherian algebras of small Gelfand-Kirillov dimension. The focus is on the interplay between their combinatorics and the algebraic structure. This yields a rich resource of examples that are of interest not only for the noncommutative ring theorists, but also for researchers in semigroup theory and certain aspects of group and group ring theory. Mathematical physicists will find this work of interest owing to the attention given to applications to the Yang-Baxter equation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 361

Добавлена в каталог: 27.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal{H}$-class      8
$\mathcal{J}$-class      8
$\mathcal{L}$-class      8
$\mathcal{R}$-class      8
$\pi$-regular closure      31
$\pi$-regular semigrou])      16
$\sigma$-invariant ideal      331
$\Sigma$-Prime ideal      331
Algebra of subexponential growth      115
Algebra, catenary      43
Algebra, finitely presented      92
Algebra, Munn      11
Algebra, PI      40
Annihilator, right, left      38
Artinian, right, left      38
Associated group      14 22
Augmentation ideal      8
Bieberbach group      217
Binomial monoid      220
Block monomial      107
Braid relation      202
Brandt semigroup      11
Cancellative semigroup      11
Catenary      43
Center      38
class      54
Classical Krull dimension      38
Classical ring of (right) quotients      39
Closure, $\pi$-regular      31
Closure, completely 0-simple      14
Closure, Zariski      33
Commutator subgroup      16
Completely 0-simple closure      1 1
Completely 0-simple semigroup      9
Completely integrally closed      55
Congruence      8
Congruence, 0-matrix      12
Congruence, least cancellative      13
Congruence, least right cancellative      13
Congruence, right      8
Corner      52
Cycle of type $k \times p$      202
Cyclic condition      261
Cyclic semigroup      7
Decomposable monoid of I-type      220
Degree function      125
Dihedral free group      57
Dimension subgroup      15
Dimension, classical Krull      38
Dimension, Gelfand — Kirillov      51
Divisorial ideal      55
Divisorial product      55
Egg-box pattern      10
Element, G-norinal      57
Element, nilpotent      16 38
Element, normal      43 95
Element, periodic      7
Equivalent orders      55
Exterior cyclic condition      228
Exterior power      34
FC-center, or finite conjugacy center      44
FC-group, or finite conjugacy group      44
Fractional ideal      58
Fractional ideal, integral      55
Fractional R-ideal      55
Full cyclic condition      262
G-normal      57
G-torsion      49
Gelfand — Kirillov dimension      51
Goldie ring      40
Graded Noetherian      18
Graded ring      47
Green's relations      8
Group of I-type      217
Group of right quotients      11
Group, $p'$      44
Group, $\mathcal{P}$-by-$\mathcal{Q}$      41
Group, associated      14 22
Group, Bieberbach      217
Group, dihedral free      57
Group, FC      44
Group, Heisenberg      79
Group, imprhnitive      241
Group, poly-$\mathcal{P}$      11
Group, polycyclic-by-finite      45
Group, primitive      241
Group, retract able      223
Group, torsion free      44
Group, unique product      48
Grouplike subsemigroup      64
Height      38
Hirsch rank      45
Homogeneous component      18
Homogeneous element      18
Homogeneous ideal      48
I-structure      198
Ideal uniform component      22
Ideal, $\sigma$-invariant      331
Ideal, $\sigma$-prime      331
Ideal, divisorial      55 58
Ideal, fractional      55 58
Ideal, homogeneous      48
Ideal, invertible      55
Ideal, maximal      38
Ideal, prime      38
Ideal, primitive      111
Ideal, semiprime      38
Imprimitive group      241
Imprimitivity, set of      241
Integral fractional ideal      55 58
Integrally closed      55
Interior cyclic condition      228
Invertible ideal      55
Irreducible module      37
Jacobson radical      38
Jacobson ring      49
Kaplansky's conjecture      224
Krull order      56
Layer      21
Left non-degenerate      202 260
Length      260
Linear semigroup      7 17
Linear semigroup, associated group of      22
Linear semigroup, ideal uniform component of      22
Linear semigroup, layer of      21
Linear semigroup, nilpotent component of      22
Linear semigroup, structural chain of      24
Linear semigroup, uniform component of      22 23
localization      39 178
Malcev nilpotent semigroup      54
Matrix units      42
Maximal ideal      38
Maximal order      55 58
Maximal subgroup      8
Module, irreducible      37
Module, semisimple      38
Module, simple      37
Module, uniform      39
Monoid of I-type      215
Monoid of left I-type      198
Monoid of skew type      259
Monoid, binomial      226
Monoid, decomposable      220
Monoid, defined by homogeneous relations      125
Monoid, finitely presented      92
Monoid, full linear      17
Monoid, group-by-abelian-by-finite      86
Monoid, order      58
Monoid, symmetric inverse      19
Monoid, weakly periodic      125
Monomial matrix      26 98
Monomial matrix over a group      31
Multipermutation solution      223
Munn algebra      11
Nil semigroup      16
Nil set      38
Nilpotent component      22
Nilpotent element      16 38
Nilpotent semigroup      16
Nilpotent set      38
Noetherian, right, left      38
Non-degenerate      260
Normal element      43 95
normalizer      101
Normalizing extension      43
Orbital      46
Order      55 58
Order, Krull      56
Order, maximal      55 58
Orders, equivalent      55
Ore condition      11
Ore set      39
Over-jumping property      266
Periodic element      7
PI algebra      40
Plinth      47
Plinth length      47
Plinth series      47
Plinth, rational      47
Poly-$\mathcal{P}$      41
Polycyclic-by-finite group      45
Polynomial identity      40
Positive cone      58
Prime ideal      38
Prime ideal, height of      38
Prime radical      38
Prime ring      38
Prime spectrum      38
Primitive group      241
Principal factor      8
Principal ideal theorem      43
Principal right ideal ring      59
Pure subgroup      47
Radical, Jacobson      38
Radical, prime      38
Rank of a matrix      17
Rank of a semigroup      52
Rational plinth      47
Reduced row elementary form      17
Reduction      227
Ree.s factor      8
Regular element      38
Retract relation      220
Retractable level      223
Right non-degenerate      202 260
Right primitive ring      158
Ring of right quotients      39
Ring, Artinian      38
Ring, catenary      43
Ring, generalized matrix      106
Ring, Goldie      40
Ring, graded      47
Ring, graded Noetherian      48
Ring, Jacobson      49
Ring, Noetherian      38
Ring, order      55
Ring, prime      38
Ring, principal right, left ideal      59
Ring, right primitive      38
Ring, semiprime      38
Ring, semiprimitive      38
Ring, semisimple      38
Ring, simple      38
Ring, strongly graded      48
Sandwich matrix      9
Semigroup identity      33
Semigroup of matrix type      9
Semigroup of matrix type, column of      9
Semigroup of matrix type, egg-box pattern of      10
Semigroup of matrix type, idempotents of      10
Semigroup of matrix type, row of      9
Semigroup of matrix type, sandwich matrix of      9
Semigroup of monomial matrices      31
Semigroup of right quotients      12
Semigroup, $\pi$-regular      16
Semigroup, 0-cancellative      12
Semigroup, 0-simple      9
Semigroup, block monomial      107
Semigroup, Brandt      11
Semigroup, cancellative      11
Semigroup, categorical at zero      12
Semigroup, completely 0-simple      9
Semigroup, completely 0-simple, annihilator-free      27
Semigroup, cyclic      7
Semigroup, linear      7 17
Semigroup, Malcev nilpotent      51
Semigroup, monomial      98
Semigroup, nil      11
Semigroup, nilpotent      16
Semigroup, normalizing      95
Semigroup, null      9
Semigroup, periodic      16
Semigroup, prime      12
Semigroup, Rees factor      8
Semigroup, regular      16
Semigroup, uniform      14
Semigroup, weakly 0-cancellative      12
Semilattice of semigroups      15
Semiprime ideal      38
Semiprime ring      38
Semiprimitive ring      38
Semisimple module      38
Semisimple ring      38
Set theoretic solution      202
Set, nil      38
Set, nilpotent      38
Simple module      37
Simple ring      38
Strongly graded ring      48
Structural chain      24
Subgroup, commutator      46
Subgroup, pure      47
Subring, homogeneous      48
Support      2
Triangular set      16
Two unique product group      48
Uniform component      22 23
Uniform module      39
Uniform semigroup, cancellative components (or parts) of      14
Unique factorization domain      57
Unique factorization ring      57
Unique product group      48
Unit group      8 40
Yang — Baxter equation      202
Yang — Baxter set theoretic solution      202
Zariski closure      33
Zariski topology      32
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