Hx@=HQ@H |oDiy Q=v}tU - Math

|}=Hx@=H Q@H |oDiy Q=v}tU
(1393
Q=y@)
An Open Problem on a Generalization of Prime Ideals in Commutative Ring
Theory
'QwB
93 2 4
KY=v u=t}B
QyD x=oWv=O
u=
Abstract
Let R be a commutative ring with identity and n be a positive integer. Anderson and Badawi, in their paper on n-absorbing ideals, dene a proper ideal I of a
commutative ring R to be an n-absorbing ideal of R, if whenever x1 xn+1 I
for x1 ; ; xn+1 R, then there are n of the xi 's whose product is in I and conjecture that !R[X ] (I [X ]) = !R (I ) for any ideal I of an arbitrary ring R, where
!R (I ) = min n : I is an n-absorbing ideal of R . In this talk, we use content formula
techniques to prove that their conjecture is true, if one of the following conditions
hold:
(1) The ring R is a Prufer domain.
(2) The ring R is a Gaussian ring such that its additive group is torsion-free.
(3) The additive group of the ring R is torsion-free and I is a radical ideal of R.
This is the open problem 30c mentioned in the paper on open problems in commutative ring theory written by Sara Glaz et al.
2
2
f
g
Simplicial Complexes Satisfying Serre's Condition as a Generalization of
Cohen-Macaulay Simplicial Complexes
'|Q=NiO}U
|O
=}v@
|
93 2 11
u}t=O}U
=yWv=O x=oWywSB
Abstract
There are several attempts to characterize Cohen-Macaulay simplicial complexes for
some special classes of simplicial complexes. This talk is a survey of these developments. As a generalization of Cohen-Macaulay simplicial complexes, we consider the
simplicial complexes, whose Stanley-Reisner ring Satises Serre's condition.
|
Q@H
www
|S r B D QO
syt
= Q@H
| y
R=
|}=yr=Ft
'`Q=R |O=y
93 2 18
QyD x=oWv=O
u=
Q@H
w
Lambda
ww w w
Ovv=t
|
Q@H
www
|S r B D QO
syt
= Q@H
| y
= Qorta Q@H |rm |iQat x@ Ckw OwHw
|S r t y m | y
R=
xvwtv OvJ |iQat x@ |v=QvNU u}=
w
Steenrod Q@
s
Q |t
s
Q |t xDi=} s}taD
CQ Y QO" } R=O B
" } R=O B
H w
O}mJ
QO
%x
Dyer-Lashof
ww w
= x} Q_v
|S r t y | y
Gorenstein Injective Envelopes of Artinian Modules
'x=wNm}v
xtwYat
Q R
=oWv=O
QO
93 3 1
= y r= x
Abstract
Let R be a commutative Noetherian ring and A an Artinian R-module. We prove
that if A has nite Gorenstein injective dimension, then A possesses a Gorenstein
injective envelope which is special and Artinian. This, in particular, yields that over
a Gorenstein ring any Artinian module possesses a Gorenstein injective envelope which
is special and Artinian.
Cohomology of Sheaves
'|Uw] OwaUt
|DWy@ O}yW x=oWv=O
O = |t
" W @
=DUtR
92 u
12
=}v@
|O
|r=
w
10
R}}=B
w |O
=}v@
|
= |v=QvNU EL=@t xt=O=
Ca=U =y x@vW GvB
=yWv=O x=oWywSB 'Qvy=@ O}yW u=O}t
=tW ur=U '(C [ } Q w | v } i C
=}
=
Q_
l R}
=yWv=O x=oWywSB
=UrH
| y
|
1 xQ
4 5 w 3 29 '3 22
QO 4 5 w 3 29 '3 22 C
=
%u tR
=mt
%u
)
=k}kLD RmQt

Download Report