We consider the irreducible carpets \( \mathfrak{A}=\{\mathfrak{A}_{r}:\ r\in\Phi\} \) of type \( F_{4} \) over an algebraical extension \( K \) of a field \( R \) such that all additive subgroups \( \mathfrak{A}_{r} \) are \( R \)-modules. The carpets, parametrized by a pair of additive subgroups, appear only in characteristic 2. This pair of additive subgroups presents (possibly different) fields up to conjugation by a diagonal element in the corresponding Chevalley group. Moreover, we establish that such carpets \( \mathfrak{A} \) are closed. Using Levchuk’s description of the irreducible carpets of Lie type of rank greater than 1 over \( K \), we show that all additive subgroups of the carpets coincide with an intermediate subfield between \( R \) and \( K \) of the carpets of types \( B_{l} \), \( C_{l} \), and \( F_{4} \) in case of the characteristic of \( K \) is not 0 and 2 whereas it is neither 0, 2, nor 3 for type \( G_{2} \) up to conjugation by a diagonal element.

我们考虑代数扩展 \ ( F_{4} \) 类型的不可约地毯 \( \mathfrak{A}=\{\mathfrak{A}_{r}:\ r\in\Phi\} \ )域\( R \ ) 的 ( K \)使得所有加性子群 \( \mathfrak{A}_{r} \)都是\( R \) -模。由一对加性子群参数化的地毯仅出现在特征 2 中。这对加性子群呈现出（可能不同的）场，直至与相应 Chevalley 群中的对角元素共轭。此外，我们确定这样的地毯\( \mathfrak{A} \)是封闭的。使用 Levchuk 对在\( K \)上秩大于 1 的李类型不可约地毯的描述 ，我们表明地毯的所有加性子群与地毯的 \( R \)和 \( K \)之间 的中间子域一致类型为 \( B_{l} \)、\( C_{l} \)和 \( F_{4} \) 的地毯 ，如果 \( K \)的特征不是 0 和 2，而它既不是0、2 或 3 对于类型 \( G_{2} \) 直至通过对角线元素共轭。