Geodesic
Serial Right Noetherian Rings
Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 22-37

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A module M is called a serial module if the family of its submodules is linearly ordered under inclusion. A ring R is said to be serial if RR as well as RR are finite direct sums of serial modules. Nakayama [8] started the study of artinian serial rings, and he called them generalized uniserial rings. Murase [5, 6, 7] proved a number of structure theorems on generalized uniserial rings, and he described most of them in terms of quasi-matrix rings over division rings. Warfield [12] studied serial both sided noetherian rings, and showed that any such indecomposable ring is either artinian or prime. He further showed that a both sided noetherian prime serial ring is an (R:J)-block upper triangular matrix ring, where R is a discrete valuation ring with Jacobson radical J. In this paper we determine the structure of serial right noetherian rings (Theorem 2.11). 
Singh, Surjeet. Serial Right Noetherian Rings. Canadian journal of mathematics, Tome 36 (1984) no. 1, pp. 22-37. doi: 10.4153/CJM-1984-003-5
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