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pro vyhledávání: '"John A. Beachy"'
Autor:
John A. Beachy
The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Features of interest include an early introduction of projective and
Autor:
John A. Beachy, Christine M. Leroux
Publikováno v:
Advances in Rings and Modules. :59-67
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5e61704f73d0968d474c38bb9a6b461e
https://doi.org/10.1090/conm/715/14404
https://doi.org/10.1090/conm/715/14404
Autor:
Abigail C. Bailey, John A. Beachy
Publikováno v:
Communications in Algebra. 45:2662-2672
We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::50f48cfbfa1c1f29d9ea796ae25d7b46
https://doi.org/10.1080/00927872.2016.1233232
https://doi.org/10.1080/00927872.2016.1233232
Autor:
Christine M. Leroux, John A. Beachy
Publikováno v:
Communications in Algebra. 44:3301-3307
It is shown that prime ideals of a Noetherian ring are linked if and only if certain corresponding prime ideals are linked in an associated Artinian ring. Furthermore, it is shown that there is a canonical linking ideal, which can be found by using a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4b9d6e58704842685b5947c74af18030
https://doi.org/10.1080/00927872.2015.1027381
https://doi.org/10.1080/00927872.2015.1027381
Autor:
John A. Beachy
Publikováno v:
Communications in Algebra. 44:1181-1195
It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion of a prime M-ideal, it is shown that this correspondence can be e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fbc29d6ec980a2b002c2540fd348ffca
https://doi.org/10.1080/00927872.2014.999934
https://doi.org/10.1080/00927872.2014.999934
Publikováno v:
Journal of the Korean Mathematical Society. 50:1271-1290
Let M be a fixed left R-module. For a left R-module X, we introduce the notion of M-prime (resp. M-semiprime) submodule of X such that in the case M=R, which coincides with prime (resp. semiprime) submodule of X. Other concepts encountered in the gen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d2cbe7c08e2dc5fda8bff9bcd710a92
https://doi.org/10.4134/jkms.2013.50.6.1271
https://doi.org/10.4134/jkms.2013.50.6.1271
Autor:
John A. Beachy
Publikováno v:
Bulletin of the Australian Mathematical Society. 69:361-367
Throughout this note, R will denote a left Noetherian ring (with identity), and S will denote a semiprime ideal of R. The study of the universal localisation RΓ(S) was initiated by P. M. Cohn, and continued by the present author (in [3, 4, 5, 6]) an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::beb25437628e31364970d64954be4ced
https://doi.org/10.1017/s0004972700036145
https://doi.org/10.1017/s0004972700036145
Autor:
John A. Beachy
Publikováno v:
Communications in Algebra. 30:4649-4676
For a left R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we investigate conditions on the module M which imply that there is a one-to-one correspondence betwee
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9962f4998dcb467a477c300f9c88b10a
https://doi.org/10.1081/agb-120014660
https://doi.org/10.1081/agb-120014660
Autor:
John A. Beachy
Publikováno v:
Communications in Algebra. 29:4919-4922
Additive rank functions have been studied for Noetherian rings by Krause. It is shown that the notion of an additive rank function can be extended to more general classes of rings, and can be used in the characterization of semiprime Goldie rings and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::baa7e4199c174bc45b78dcf95ce23cb0
https://doi.org/10.1081/agb-100106793
https://doi.org/10.1081/agb-100106793
Autor:
John A. Beachy, Abigail C. Bailey
Publikováno v:
Journal of Algebra and Its Applications. 14:1550059
We determine conditions under which a generalized triangular matrix ring has finite reduced rank, in the general torsion-theoretic sense. These are applied to characterize certain orders in Artinian rings, and to show that if each homomorphic image o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::89db2721bc30d42edeb3517654795e25
https://doi.org/10.1142/s0219498815500590
https://doi.org/10.1142/s0219498815500590