| Exterior algebras,which are defined in a vector space V, are a class of very important algebra. Exterior algebras and their modules, with strong application background.There is a series of study on exterior algebras and their modules re-cently, however, the extension of two modules is an elementary and very interesting part of the study of modules.In this paper, we called such linear modules-their representation matrix has the following form:t-linear module of type (a, b, c)and of complexity one with cyclic length m, in which, t is row mark of the first column,in which c appears;and minimal linear module of type (a, b) and of complexity two with cyclic length n respectively.In this paper, we make efforts to study on the non-linear extension of two t-or s-linear modules of complexity one and of type(a,b,c) with different cyclic length, and the non-linear extension of two linear modules--one is minimal linear module of complexity two and of type(a, b) with cyclic length m, another is t-linear module of complexity one and of type (a, b, c)with cyclic length n.We still apply the method of representation matrix in this paper. Firstly, we calculate the representation matrix of non-linear extension modules, and thus discuss terms of isomorphism.Theorem 3.1 prove that there is only trivial non-linear extension between t-(or s-)linear modules of type (a, b, c) and of complexity one with different cyclic length respectively. Theorem 3.1 and theorem 4.1 prove that representation matrix and isomorphism terms of nonlinear extension modules between t-linear module of complexity one and of type (a, b, c) with cyclic length n. |
