Diagonal equivalence of matrices over a finite local ring

AbstractLetR/R be a quadratic extension of finite, commutative, local and principal rings of odd characteristic. Denote byUn(R) the unitary group of ranknassociated toR/R. The Weil representation ofUn(R) is defined and its character is explicitly computed.

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Artinian Local Rings Whose Annihilating-ideal Graphs Are Star Graphs

Algebra Colloquium ◽

10.1142/s1005386715000073 ◽

2015 ◽

Vol 22 (01) ◽

pp. 73-82 ◽

Cited By ~ 2

Author(s):

Houyi Yu ◽

Tongsuo Wu ◽

Weiping Gu

Keyword(s):

Local Ring ◽

Complete Characterization ◽

Local Rings ◽

Star Graph ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Star Graphs ◽

Finite Local Ring ◽

Necessary And Sufficient

In this paper, a necessary and sufficient condition is given for a commutative Artinian local ring whose annihilating-ideal graph is a star graph. Also, a complete characterization is established for a finite local ring whose annihilating-ideal graph is a star graph.

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UNITARY GROUPS OVER LOCAL RINGS

Journal of Algebra and Its Applications ◽

10.1142/s021949881350093x ◽

2013 ◽

Vol 13 (02) ◽

pp. 1350093 ◽

Cited By ~ 2

Author(s):

J. CRUICKSHANK ◽

A. HERMAN ◽

R. QUINLAN ◽

F. SZECHTMAN

Keyword(s):

Local Ring ◽

Unitary Group ◽

Quadratic Extension ◽

Unitary Groups ◽

Weil Representation ◽

Local Rings ◽

Hermitian Forms ◽

Finite Local Ring

We study hermitian forms and unitary groups defined over a local ring, not necessarily commutative, equipped with an involution. When the ring is finite we obtain formulae for the order of the unitary groups as well as their point stabilizers, and use these to compute the degrees of the irreducible constituents of the Weil representation of a unitary group associated to a ramified quadratic extension of a finite local ring.

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CONGRUENCE OF SYMMETRIC INNER PRODUCTS OVER FINITE COMMUTATIVE RINGS OF ODD CHARACTERISTIC

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972717000405 ◽

2017 ◽

Vol 96 (3) ◽

pp. 389-397

Author(s):

SONGPON SRIWONGSA

Keyword(s):

Commutative Ring ◽

Local Ring ◽

Finite Rank ◽

Congruence Class ◽

Commutative Rings ◽

Inner Products ◽

Finite Local Ring ◽

Finite Commutative Ring ◽

Finite Commutative Rings

Let $R$ be a finite commutative ring of odd characteristic and let $V$ be a free $R$-module of finite rank. We classify symmetric inner products defined on $V$ up to congruence and find the number of such symmetric inner products. Additionally, if $R$ is a finite local ring, the number of congruent symmetric inner products defined on $V$ in each congruence class is determined.

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