> ,.+{` bjbjFF 7,,,,,,,,,, """"""$hjFB,,BBF,,[B,, B , p`F q0iiip,
|(,,,FF
,,,BBBB$$Dear Colleagues,
Las July I had the (wonderful) opportunity to supervise the work of the following students:
Joel Louwsma (Univ. of Michigan),
Adilson Eduardo Presoto (Univ. of Sao Carlos, Brazil) Alan Tarr (pomona College) Their work resulted in an interesting result that was written and (I hope
so) submitted to you. The manuscript is entitled Codimension Sequence of the Grassmann Algebra
I supervised them during their REU project in July 2004 here at the State University of Campinas, Brazil.
The paper studies polynomial identities for the Grassmann algebra. These are well understood and constitue one of the keystones of the theory of algebras with polynomial identities.
The main contribution of the paper is the computing the codimension sequence of the ideal of the identities of the Grassmann algebra. This result is classical and it was proved in 1974 by Krakowski and Regev. The present paper gives a new proof of the theorem of Krakowski and Regev. The proof is based on some properties of the matrix rank, and combinatorics.
In fact the reader is not supposed to know much about the Grassmann algebra, and not anything about polynomial identities. Some basic linear is required although.
The paper is well written and the references are adequate.
The essential part, the maths, is serious and one cannot compare it to some routine homework. The result is deep and the proof is interesting. It differs significantly from the original one, and might be generalized in certain directions.
In my opinion the paper satisfies the requirements of your journal and its publishing would be something desirable.
The students were undergraduates while working on the project. (And to the best of my knowledge they still are undergraduates.)
My name and address: Plamen Koshlukov, Department of Mathematics, IMECC, UNICAMP, P.O. Box 6065, 13083-970 Campinas, SP, Brazil.
If you need some further information please do contact me, preferably by e-mail.
Cordially,
Plamen Koshlukov
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Plamen Koshlukov
Departamento de Matematica ||phone (++55)(19) 3788 60 02
IMECC - UNICAMP, Cx. P. 6065 ||fax (++55)(19) 3289 57 66
Campinas - 13083 - 970 - SP ||fax (++55)(19) 3289 58 08
BRASIL ||e-mail plamen@ime.unicamp.br
h9)hhCJOJQJ^JaJn+
VWYZY 7$8$H$gdh 7$8$H$gdh50P:ph/ =!"#$%@@@NormalCJ_HaJmH sH tH DA@DDefault Paragraph FontRi@RTable Normal4
l4a(k@(No Listn+VWYZY000000000000000000000000000000000n+VWYZYy0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0y0YZ
a
b
}c
3"d
te
4ʐf
Đg
Ðh
ːi
!j
D!k
l
< m
Ȑn
so
L ||**CQQ
27KWW
B*urn:schemas-microsoft-com:office:smarttagscountry-region:*urn:schemas-microsoft-com:office:smarttagsStreet;*urn:schemas-microsoft-com:office:smarttagsaddress8*urn:schemas-microsoft-com:office:smarttagsCity=*urn:schemas-microsoft-com:office:smarttags PlaceType=
*urn:schemas-microsoft-com:office:smarttags PlaceName9*urn:schemas-microsoft-com:office:smarttagsplace{
\gx%.V_'gpuzNW
CK+/9jl+-HJ33333\}eD&u=^)&mgKm B!,a!v!m."8"R#VI$a&9)
*0 *5u*|,- F.| /H/B06)0
1C2g2G3;4;s4o.5K6Q_6u6+7J8;E=x?BzBa1ChDEIEqFG(-G?/IPIxJSIKLyM
N*OQEPV_VdW%jX>QY|Y1ZxZ'[0d\6_lN_(U_X_3dEf: g(hgh#h~h7=i+lMlQmt}m2s]tTuu,w,|w|c}3Q$sp}{C03`8'7~V$la3Oqo4;A4emO?'"($Ve DiBqGcP#.^8CR)os!-|%=i0O'7O1OO&\A{0:!]M~x 8'e\ueFvOws,r