Left modules notation with a left subscript?

In summary, Berrick and Keating's book on rings and modules discusses the use of left-subscript notation in left modules, where the subscript is placed to the left. An example of this notation is seen in End(M), where M is a left module over E. To achieve this in Latex, use the notation {}_EM to produce ${}_EM$.
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I am reading Berrick and Keating's book on rings and modules.

Berrick and Keating indicate a right module over a ring \(\displaystyle R\) as \(\displaystyle M_R\), but in a left module the subscript is to the left ... can someone help me with the Latex script to achieve this?

An example of "left-subscript" notation appears in the following text from Berrick and Keating's book, where they refer to End(\(\displaystyle M\)) where \(\displaystyle M\) is a left module over \(\displaystyle E\).View attachment 3074
Hope someone can help?

Peter
 
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Peter said:
I am reading Berrick and Keating's book on rings and modules.

Berrick and Keating indicate a right module over a ring \(\displaystyle R\) as \(\displaystyle M_R\), but in a left module the subscript is to the left ... can someone help me with the Latex script to achieve this?

An example of "left-subscript" notation appears in the following text from Berrick and Keating's book, where they refer to End(\(\displaystyle M\)) where \(\displaystyle M\) is a left module over \(\displaystyle E\).View attachment 3074
Hope someone can help?

Peter

Sure Peter, use {}_EM to produce ${}_EM$.
 

FAQ: Left modules notation with a left subscript?

What is a left module notation with a left subscript?

A left module notation with a left subscript is a way of denoting the action of a left module on an element. It is typically written as a left subscript to the element, with the module acting as a multiplier.

How is a left module notation with a left subscript different from a right subscript?

In a left module notation, the module acts on the left side of the element, while in a right module notation, the module acts on the right side. This can affect the order of multiplication and the resulting outcome.

What is the purpose of using a left subscript in left module notation?

A left subscript is used in left module notation to clearly indicate the direction of the module action and to avoid confusion in cases where both left and right module notations are used.

How is a left module notation with a left subscript used in linear algebra?

In linear algebra, a left module notation with a left subscript is commonly used to represent the action of a linear transformation on a vector space. It allows for a concise and consistent notation for expressing linear transformations and their effects on vectors.

Are there any other notations that are commonly used for left modules?

Yes, in addition to left module notation with a left subscript, there is also the right module notation with a right subscript and the dot notation, where the module is written as a dot to the right of the element. However, the choice of notation often depends on personal preference and the conventions of the field of study.

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