PS-modules over generalized Malcev-Neumann series

Abstract

In [1], the rst author introduced a new class of extension rings called the generalized Malcev-Neumann series ring $R((S;\sigma;\tau))$ with coeffcients in a ring $R$ and exponents in a strictly ordered monoid $S$ which extends the usual construction of Malcev-Neumann series rings. The conditions under which the generalized Malcev-Neumann series modüle $M((S))_{R((S;\sigma;\tau))}$ is a PS-module are investigated in the present paper.

Keywords

• PS-module,generalized Malcev-Neumann series rings

References

1. M. Farahat, Generalized Malcev-Neumann series modules with the Beachy-Blair condition, Algebra (Hindawi Publishing Corporation), Article ID 595274, (2015), doi:10.1155/2015/595274.
2. W. Nicholson and J. Watters, Rings with projective socle, Proc. Amer. Math. Soc., 102, (1988), 443-450.
3. J. Zelmanowitz, Regular modules, Trans. Amer. Math. Soc., 163, (1972), 341-355.
4. Weimin Xue, Modules with projective socles, Riv. Mat. Univ. Parma, 1(5), (1992), 311-315.
5. Dingguo Wang, Modules with at socles and almost excellent extensions, Acta Math. Viet- nam., 21(2), (1996), 295-301.
6. A. Malcev, On embedding of group algebras in a division algebra (in russian), Dokl. Akad. Nauk, (1948), 14991501.
7. B. Neumann, On ordered division rings. Trans. Amer. Math. Soc., 66, (1949), 202252.
8. A. Kelarev, Ring Constructions and Applications, World Scientic, River Edge, New York, 2002.

9. R. Zhao and Y. Jiao, Principal quasi-baerness of modules of generalized power series, Taiwanese J. Math., 15(2), (2011), 711-722.