Regular projective resolutions OF SEMIMODULES

Ho Xuan Thang, Nguyen Xuan Tuyen



In this paper, we present an approach version of semimodule homologies by regular projective resolutions such as define a concept of a regular projective resolution, prove the comparison theorem for semimodules by these resolutions and based them provide cohomology monoids of semimodules.


J. Y. Abuhlail, S. N. Il'in, Y. Katsov and T. G. Nam, On V-Semirings and Semirings all of whose Cyclic Semimodules are Injective, Comm. Algebra 43(2015), 4632-4654.

H. M. J. Al-Thani, A note on projective semimodules, Kobe J.Math., 12 (1995), 89- 94.

J. Golan, Semirings and their Applications, Kluwer Academic Publishers, Dordrecht-Boston-London, 1999.

A. Patchkoria, On derived functors of semimodule-valued functors, Trudy Tbilis. Mat. Inst. Pazmadze, 83(1986), 60-75 (Russian).

Nguyen Xuan Tuyen. On the homology bifunctors over semimodules. Advances in Algebra , World Scientific, 2004, 450-456.

N.X. Tuyen, A theory of semirings and semimodules, Hue Univ. Publishing House, 2010.

H. S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Am. Math. Soc. 40(1934), 914-920.