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I am reading Paul E. Bland's book "Rings and Their Modules ...
Currently I am focused on Section 2.3 Tensor Products of Modules ... ...
I need some help in order to fully understand the Remark that Bland makes on Pages 65 66
Bland's remark reads as follows:
Question 1
In the above text by Bland we read the following:
"... ... but when ##g## is specified in this manner it is difficult to show that it is well defined ... ... "
What does Bland mean by showing ##g## is well defined and why would this be difficult ... ...
Question 2
In the above text by Bland we read the following:
"... ... Since the map ##h = \rho' ( f \times id_N )## is an Rbalanced map ... ... "
Why is ##]h = \rho' ( f \times id_N )## an Rbalanced map ... can someone please demonstrate that this is the case?
Hope someone can help ... ...
Peter
=============================================================================
The following text including some relevant definitions may be useful to readers not familiar with Bland's textbook... note in particular the Rmodule in Bland's text means right Rmodule ...
Currently I am focused on Section 2.3 Tensor Products of Modules ... ...
I need some help in order to fully understand the Remark that Bland makes on Pages 65 66
Bland's remark reads as follows:
Question 1
In the above text by Bland we read the following:
"... ... but when ##g## is specified in this manner it is difficult to show that it is well defined ... ... "
What does Bland mean by showing ##g## is well defined and why would this be difficult ... ...
Question 2
In the above text by Bland we read the following:
"... ... Since the map ##h = \rho' ( f \times id_N )## is an Rbalanced map ... ... "
Why is ##]h = \rho' ( f \times id_N )## an Rbalanced map ... can someone please demonstrate that this is the case?
Hope someone can help ... ...
Peter
=============================================================================
The following text including some relevant definitions may be useful to readers not familiar with Bland's textbook... note in particular the Rmodule in Bland's text means right Rmodule ...
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