Jukl, Marek Grassmann formula for certain type of modules. (English) Zbl 0860.13006 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 34, 69-74 (1995). Let \(A\) be a commutative local ring whose maximal ideal has finite Loewy length. The author extends to finitely generated free \(A\)-modules several results which are well-known for finite-dimensional vector spaces. For example, linearly independent sets of elements can be extended to bases, submodules are direct summands, hyperplanes are kernels of homomorphisms onto \(A\). The author also proves an analogue of the rank-nullity theorem. Reviewer: Ph.Schultz (Perth) Cited in 6 Documents MSC: 13C10 Projective and free modules and ideals in commutative rings 13E15 Commutative rings and modules of finite generation or presentation; number of generators 15A03 Vector spaces, linear dependence, rank, lineability Keywords:finitely generated free modules; Loewy length × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] McDonald B. R.: Geometric algebra over local rings. Pure and applied mathematics, New York, 1976. · Zbl 0346.20027 [2] Anderson F. W., Fuller F. K.: Rings and Categories of Modules. Springer Verlag, New York, 1973. [3] Machala F.: Fundamentalsätze der projektiven Geometrie mit Homomorphismus. Rozpravy ČSAV, řada matem. a přír. věd 90, sešit 5, Academia, Praha, 1980. · Zbl 0457.51003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.