Let $\tilde{U}_z(\hat{gl_n})$ be the Garland integral form of $U(\hat{gl_n})$ introduced by Garland, where $U(\hat{gl_n})$ is the universal enveloping algebra of $\hat{gl_n}$. Using Ringel-Hall algebras, one can naturally construct an integral form, denoted by $U_z(\hat{gl_n})$, of $U(\hat{gl_n})$. We prove that $\tilde{U}_z(\hat{gl_n})$ coincides with $U_z (\hat{gl_n})$. Let k be a commutative ring with unity. Assume p=char k>0. We call $U_k(\hat{gl_n}):=\tilde{U}_z(\hat{gl_n})\otimes k$ the hyperalgebra of $\hat{gl_n}$. For $h\geq 1$, we use Ringel--Hall algebras to construct a certain subalgebra, denoted by $u_{\Delta}(n)_h$, of $ U_k(\hat{gl_n})$. The algebra $u_{\Delta}(n)_h$ is the affine analogue of the restricted enveloping algebra of $gl_n$ over $F_p$. We will give a realization of $u_{\Delta}(n)_h$ for each $h\geq 1$. Using $u_{\Delta}(n)_h$, we construct a certain subalgebra, denoted by $u_{\Delta}(n, r)_h$, of affine Schur algebras over k. The algebra $u_{\Delta}(n, r)_h$ is the affine analogue of little Schur algebras.

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