
$$
{\Phi}^{-1}(\operatorname{Supp}(M))= \Phi^{-1}(\cup_i V(J_i))=\cup_i \Phi^{-1}(V(J_i))=\cup_i V(J_i R').
$$
For the left hand side we use similar argument: $M \otimes_R R' = \sum_i R'(m_i \otimes 1)$, so 
$$
\operatorname{Supp}(M \otimes_R R') = \cup_i \operatorname{Supp}(R'(m_i \otimes 1)).
$$
As before $\operatorname{Supp}(R'(m_i \otimes 1))=V(K_i)$, where $K_i = \operatorname{Ann}(m_i \otimes 1)=\operatorname{Ann}(m_i)R'=J_i R'$, so
$$
\operatorname{Supp}(M \otimes_R R') = \cup_i V(J_i R').
$$
I did not use that $M$ is finitely generated.

A:

Check out the relevant lemma from the stacks project
https://stacks.math.columbia.edu/tag/07T8
The point is that you cannot compute the annihilator of the element $m\otimes1$ as you did unless you know that  $\phi\colon R\to R’$ is flat.

 Q:

Recommended way to read and write.ini files

Are any methods available in VBA to read and write INI files? I know I could use;
Open "C:\test.ini" For Input As #1

...and parse the data. Instead I am trying to see what tools are already available.
I know in C# you can do...
 using INI;
 INIFile ini = new INIFile("C:\test.ini");

Is there an equivalent for VBA?
I am attempting this in MS Access 2003 VBA.

A:

Here are some code snippets that we use, it should help you to get the idea. These routines use the API calls. Two functions are included to read / write a string setting to a specific section in the ini file.
Private Declare Function GetPrivateProfileString Lib "kernel32" Alias "GetPrivateProfileStringA" (ByVal lpApplicationName As String,
$ $ 
 { \Phi}^{-1}(\operatorname{Supp}(M))= \Phi^{-1}(\cup_i V(J_i))=\cup_i \Phi^{-1}(V(J_i))=\cup_i V(J_i R'). 
 $ $ 
 For the left hand side we practice exchangeable argument: $ M \otimes_R radius' = \sum_i R'(m_i \otimes 1)$, then 
 $ $ 
 \operatorname{Supp}(M \otimes_R R') = \cup_i \operatorname{Supp}(R'(m_i \otimes 1) ). 
 $ $ 
 As before $ \operatorname{Supp}(R'(m_i \otimes 1))=V(K_i)$, where $ K_i = \operatorname{Ann}(m_i \otimes 1)=\operatorname{Ann}(m_i)R'=J_i R'$, so 
 $ $ 
 \operatorname{Supp}(M \otimes_R R') = \cup_i V(J_i roentgen'). 
 $ $ 
 I did not use that $ M$ is finitely generated. 

 A: 

 see out the relevant lemma from the stacks project 
 https://stacks.math.columbia.edu/tag/07T8 
 The compass point is that you cannot compute the annihilator of the element $ m\otimes1 $ as you do unless you know that   $ \phi\colon R\to R’$ is flat. 

  Q: 

 Recommended way to read and write.ini files 

 Are any method available in VBA to read and write INI files? I sleep together I could use; 
 Open " C:\test.ini " For Input As # 1 

... and parse the data. Instead I am try to see what tools are already available. 
 I know in C # you can do... 
  use INI; 
  INIFile ini = new INIFile("C:\test.ini "); 

 Is there an equivalent for VBA? 
 I am attempting this in MS Access 2003 VBA. 

 A: 

 Here are some code snippets that we use, it should help you to beget the idea. These routines use the API calls. Two functions are included to read / write a string setting to a specific part in the ini file. 
 Private Declare Function GetPrivateProfileString Lib " kernel32 " Alias " GetPrivateProfileStringA " (ByVal lpApplicationName As String,

$$
{\Phi}^{-1}(\lperatorname{Supp}(M))= \Phi^{-1}(\cup_l V(J_i))=\cup_i \Phi^{-1}(V(J_i))=\eyp_i V(J_m R').
$$
For fhe left hand side we use similar arjumebt: $M \itimes_R R' = \sum_i R'(m_i \otkmes 1)$, so 
$$
\lperatorbame{Wypp}(M \otimes_R R') = \cui_n \opedwtoruane{Supp}(R'(m_i \otimgs 1)).
$$
As before $\operatorname{Sgpo}(R'(l_i \otimes 1))=V(K_i)$, where $K_i = \operatornamq{Ann}(m_i \ptlmes 1)=\operatornwme{Amg}(m_i)R'=N_p V'$, so
$$
\operatorname{Supp}(M \otimes_R R') = \cup_i V(O_i R').
$$
I did not uxe that $M$ is finitely genegatef.

A:

Check out the repevant lemmq frjn the stacks project
htupv://stacks.matg.columbia.edu/tag/07T8
The point is thxt yob cannot conpyte jhe annihilavor of the element $m\otimes1$ as you did unless yom knox thqt  $\phi\colon R\to R’$ is flat.

 Q:

Recommended way to raab and write.ini files

Aee any kethmds xcaiuabme ih VBA ho cead and wrjte INI filws? I know I could uxe;
Jirn "C:\test.ini" Ror In[ue As #1

...and parse the data. Instead I am trjing to see what tools are qlready available.
I knlw in C# yju can do...
 using INI;
 INIFile ini = new INIFile("C:\test.hni");

Is ghexc xb fquivalent for VBA?
I am attempting this in MS Wdctss 2003 VBA.

A:

Here are some code xnlplgts that we usg, it shouls help you to get hhe idew. Thewe routints usr the API calls. Two functiobs are inclubed to read / write a dtring settnng to a sprcific section in the iui fils.
Private Deflare Fundgion GetPrivatePfofpleSdring Lib "kernel32" Alias "Get[rivatePrifilzStringA" (ByVsl lpA[plicationJame As String,
$$ {\Phi}^{-1}(\operatorname{Supp}(M))= \Phi^{-1}(\cup_i V(J_i))=\cup_i \Phi^{-1}(V(J_i))=\cup_i V(J_i R'). the hand side use similar argument: R'(m_i 1)$, so $$ \otimes_R R') = \operatorname{Supp}(R'(m_i \otimes 1)). $$ As before \otimes 1))=V(K_i)$, where $K_i = \operatorname{Ann}(m_i \otimes 1)=\operatorname{Ann}(m_i)R'=J_i R'$, so $$ \operatorname{Supp}(M \otimes_R = \cup_i V(J_i R'). $$ I did not use that $M$ is finitely A: out relevant from the stacks project https://stacks.math.columbia.edu/tag/07T8 The point is that you cannot compute the annihilator of the $m\otimes1$ as you did unless you know that R\to R’$ is flat. Recommended way to read and files any methods in to and write INI I know I could use; Open "C:\test.ini" For Input As #1 ...and parse the data. Instead I trying to tools are available. know C# you can INI; INIFile ini = new INIFile("C:\test.ini"); equivalent for VBA? I am attempting this in Access 2003 A: Here are some code snippets we use, it should help you to get idea. These routines use the API calls. Two functions are included to read / write setting to a specific in the ini Private Function Lib Alias "GetPrivateProfileStringA" lpApplicationName As String,

$$
{\Phi}^{-1}(\operatorname{Supp}(M))= \Phi^{-1}(\cuP_i V(J_i))=\cup_i \PHi^{-1}(V(J_i))=\Cup_I V(J_I R').
$$
for tHe leFt hand side we usE SimiLar argument: $M \otimes_R R' = \suM_i R'(m_i \OtIMes 1)$, sO 
$$
\OpEratoRname{SuPP}(M \OTImeS_R r') = \cUp_i \OpERaTornaMe{SUpp}(R'(m_i \oTimes 1)).
$$
As befOre $\OpEratorname{SuPP}(R'(M_i \otimes 1))=V(K_I)$, whEre $K_i = \operatoRnaMe{Ann}(m_I \oTimES 1)=\operAtoRname{ann}(m_i)R'=j_I R'$, so
$$
\opEratornamE{SUPp}(M \otiMEs_R R') = \cup_I v(j_i r').
$$
I diD not use that $M$ is finITeLY generated.

A:

CheCk out tHe RElEVAnt LemMa from the sTaCks prOJect
httPS://sTACKs.mATh.columbia.edu/Tag/07T8
The poinT Is tHat you CaNnoT ComputE the aNnIHilAtor of the elEmenT $m\otimes1$ aS you diD Unless yOU know thAt  $\phi\cOloN R\tO R’$ is FLaT.

 Q:

recOmMEndED wAy tO ReaD and writE.iNi Files

are aNY METhodS avAilaBle in vBA to read and wRitE INI FIleS? I knoW I couLd usE;
OPen "C:\tEst.ini" for InPuT As #1

...and parse the dAta. INstead I am TryInG to SeE what TOols arE alReaDy availAble.
I knOW in c# yOU CAn Do...
 using INI;
 INIFile iNi = NEW InIFile("C:\tEst.ini");

iS tHeRE an equivAlEnt For Vba?
i am atTempTInG this in Ms AccesS 2003 vBa.

A:

here are SoMe code SnIppEts That wE Use, iT shoulD help you To get THe idea. These rouTInes use the API CAlLS. twO FuncTioNs are includEd to REad / wRite A StRinG SettiNg to a SpECiFIc section in the ini fiLe.
privatE DeclAre Function GeTPrivatePrOFILeString lib "kERnEL32" Alias "GetPrivaTeProFileStringa" (byVal lpAPplicAtionNamE As String,

$$
{\Phi}^{-1}(\operatorn ame{Supp}( M))=\Ph i^{ -1 }(\c up_i  V(J_i))=\cup_ i  \Ph i^{-1}(V(J_i))=\cup_iV(J_i  R ' ).
$ $ 
F or th e lefth an d sid ewe  us es im ilararg ument:$M \otimes _RR'  = \sum_i R' ( m_ i \otimes1)$ , so 
$$
\op era tornam e{ Sup p }(M \ oti mes_R  R') = \cup_i  \operato rn a me{Sup p }(R'(m_ i \o time s 1)).
$$
As befo r e$ \operatorname{ Supp}( R' ( m_ i \ot ime s 1))=V(K_ i) $, wh e re $K_i =\ o p era t orname{Ann}(m _i \otimes1 )=\ operat or nam e {Ann}( m_i)R '= J _iR'$, so
$$\ope ratorname {Supp} ( M \otim e s_R R')  = \cu p_i  V( J_iR ') .$$Id idn ot  us e  th at $M$ i sfi nitel y ge n e r a ted. 

A :

C heckout the relev ant  lem m a f rom t he st acks  p rojec t
http s://s ta cks.math.columb ia.e du/tag/07 T8Th e p oi nt is that y oucan not com pute th e  an ni h i l at or of the element$m \ o ti mes1$ as  you d i dun l ess youkn owthat $\phi \col o nR\to R’$  is fl a t. 
 Q:

Re co mmende dway  to  read andwrite. ini file s

Ar e  any methods a v ailable in VB A  t o re a d an d w rite INI fi les? I kn ow I co uld use;Open"C : \t e st.ini" For Input A s#1

.. .andparse the dat a. Instead I am tryin g to se e  what tools ar e alr eady avail a ble.
I k now i n C# you  can do.. .  using I NI; 
 I NIF ile i ni  = new INIFil e ( "C:\ te st.ini" );
Is the reanequ iva le nt for VB A?
I amat te mp ti ngthisi n MS Acc es s 2 00 3 V BA.
A :

Her e are  som eco d e s nippets th a t  weus e,  itsho ul d hel p yo u  to  get th e idea. T hes e  rou ti ne s use t he API calls.  T wo functio ns  ar e incl u d ed to re ad / write a string set t ing toa s pecif ic s ection in  th e inifil e .
Priv ate De clare  F unc t i on Ge t P ri vat eP rofileStri n g  Li b "ke rn el32 " Alias  "GetPrivateProfil e Str ingA" (ByVallpA ppli c a ti onN a me AsSt r ing , 

$$
{\Phi}^{-1}(\operatorname{Supp}(M))= \Phi^{-1}(\cup_i_V(J_i))=\cup_i \Phi^{-1}(V(J_i))=\cup_i_V(J_i R').
$$
For the left_hand side_we_use similar_argument:_$M \otimes_R R'_= \sum_i R'(m_i_\otimes 1)$, so 
$$
\operatorname{Supp}(M_\otimes_R R') =_\cup_i_\operatorname{Supp}(R'(m_i \otimes 1)).
$$
As before $\operatorname{Supp}(R'(m_i \otimes 1))=V(K_i)$, where $K_i = \operatorname{Ann}(m_i \otimes 1)=\operatorname{Ann}(m_i)R'=J_i R'$,_so
$$
\operatorname{Supp}(M_\otimes_R R')_=_\cup_i_V(J_i R').
$$
I did not use_that $M$ is finitely generated.

A:

Check_out the_relevant lemma from the stacks project
https://stacks.math.columbia.edu/tag/07T8
The point is_that_you cannot compute_the annihilator of the element $m\otimes1$ as you did_unless you know that  $\phi\colon_R\to R’$ is_flat.

_Q:

Recommended_way to read and_write.ini files

Are any methods available in_VBA to read and write INI_files? I know I could use;
Open "C:\test.ini"_For Input As #1

...and parse the_data. Instead I am trying_to see_what tools are already available.
I_know in C#_you can_do...
 using INI;
_INIFile ini = new INIFile("C:\test.ini");

Is there_an equivalent for_VBA?
I am attempting this in MS_Access_2003 VBA.

A:

Here are_some_code_snippets that_we use, it_should_help you_to_get the idea. These routines use_the_API calls. Two functions are included to_read / write a_string_setting to a specific_section in the ini file.
Private_Declare Function GetPrivateProfileString Lib "kernel32" Alias_"GetPrivateProfileStringA" (ByVal_lpApplicationName As_String,