# Definition talk:Linear Combination

In this definition, should $R$ not be a ring with unity, so $M$ is a unitary module? As the definition stands now, each element of the sum:

- $\ds \sum_{k \mathop = 1}^n \lambda_k a_k$

consists of one scalar and one element of $M$. If $R$ does not have a multiplicative identity element $1_R$, then each $a_k$ gets multiplied with a non-identity. This leads to problems - for instance, you can construct an example with $x \in M$ where $x \notin \map \span x$.

I have checked some of theorem that deals with $R$-modules and linear combinations, and the ones that have proofs, like Submodule Test, Generated Submodule is Linear Combinations and Subset of Linearly Independent Set is Linearly Independent, all refer to $M$ as an unitary $R$-module

How do the sources (I presume Seth Warner's *Modern Algebra* is the main source) define the ring $R$? --Anghel (talk) 21:51, 3 January 2023 (UTC)

- I'll have to get back to you on that. --prime mover (talk) 21:54, 3 January 2023 (UTC)