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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:

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 ... ...

In the above text by Bland we read the following:

"... ... Since the map ##h = \rho' ( f \times id_N )## is an R-balanced map ... ... "

Why is ##]h = \rho' ( f \times id_N )## an R-balanced 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 R-module in Bland's text means right R-module ...

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 R-balanced map ... ... "

Why is ##]h = \rho' ( f \times id_N )## an R-balanced 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 R-module in Bland's text means right R-module ...

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