粘上
发表于 2025-3-21 18:37:25
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积云
发表于 2025-3-21 20:16:42
Sigma Cyclic and Serial Rings ring is decomposable into a finite product of Artinian and (semi)prime rings (25.3.5). This is reminiscent of the theorems of Chatters (20.30) for hereditary rings, and Krull-Asano-Goldie 20.37, for principal ideal rings, and, in fact, Robson’s general method (20.35) used to prove these also applies here.
杠杆支点
发表于 2025-3-22 03:52:31
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Cardioplegia
发表于 2025-3-22 05:55:58
Quasinjective Modules and Selfinjective Ringsulo annihilator 19.14A. Over a right Artinian ring, any QI right module is finendo and conversely 19.16. Thus, every faithful quasinjective over a right Artinian ring is injective 19.15, a result which holds for finitely generated faithful modules over commutative rings 19.17.
VICT
发表于 2025-3-22 08:57:38
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使坚硬
发表于 2025-3-22 15:15:01
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纠缠,缠绕
发表于 2025-3-22 18:57:25
https://doi.org/10.1007/978-3-322-96680-3rphism .. This notion is dual to that of injective hull, and yet, although each .-module has an injective hull, projective covers of modules may fail to exist. For example, as is shown in this chapter, a necessary condition that every right .-module have a projective cover is that ./rad . be semisimple, and rad . be a nil ideal.
ALT
发表于 2025-3-22 21:56:33
Semilocal Rings and the Jacobson Radicalmposition Theorem 18.18; (7) the basic module and ring 18.21–23; (8) the Chinese remainder theorem 18.30–32 and primary decomposable rings 18.36–37; and (9) the characterization 18.47 of rings with semilocal right quorings. (As defined by (I, p. 4.10), . is semilocal if ./rad . is semisimple. Also see 18.10A.)
持续
发表于 2025-3-23 03:08:46
Projective Covers and Perfect Ringsrphism .. This notion is dual to that of injective hull, and yet, although each .-module has an injective hull, projective covers of modules may fail to exist. For example, as is shown in this chapter, a necessary condition that every right .-module have a projective cover is that ./rad . be semisimple, and rad . be a nil ideal.
Enrage
发表于 2025-3-23 06:15:06
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