PS-modules over generalized Malcev-Neumann series

Year 2017, Volume: 46 Issue: 5, 829 - 834, 01.10.2017

Mohamed A. Farahat Naif S. Al-harthy

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

• 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.
• W. Nicholson and J. Watters, Rings with projective socle, Proc. Amer. Math. Soc., 102, (1988), 443-450.
• J. Zelmanowitz, Regular modules, Trans. Amer. Math. Soc., 163, (1972), 341-355.
• Weimin Xue, Modules with projective socles, Riv. Mat. Univ. Parma, 1(5), (1992), 311-315.
• Dingguo Wang, Modules with at socles and almost excellent extensions, Acta Math. Viet- nam., 21(2), (1996), 295-301.
• A. Malcev, On embedding of group algebras in a division algebra (in russian), Dokl. Akad. Nauk, (1948), 14991501.
• B. Neumann, On ordered division rings. Trans. Amer. Math. Soc., 66, (1949), 202252.
• A. Kelarev, Ring Constructions and Applications, World Scientic, River Edge, New York, 2002.
• R. Zhao and Y. Jiao, Principal quasi-baerness of modules of generalized power series, Taiwanese J. Math., 15(2), (2011), 711-722.