A Class of rings is said to be weakly hereditary if 0≠I△R∈ implies 0≠I^n∈ for some positive integer n, which generalizes the concept of heredity but other than that of regularity. In §2 the properties of su...A Class of rings is said to be weakly hereditary if 0≠I△R∈ implies 0≠I^n∈ for some positive integer n, which generalizes the concept of heredity but other than that of regularity. In §2 the properties of such class and its essential cover are studied. In §3 the upper radicals determined by them are investigated. At the same time the 'Problem 42, 44 and 55' of Szasz [7] are discussed. In §4 two examples are given, which show that the concept of weak heredity is independent of that of regularity.展开更多
In this paper an improved multi_scale estimation method of signal is gaven.The detail signals on each scale are further more decomposed with wavelet transform.The subdetail signals and subsmoothing signals are process...In this paper an improved multi_scale estimation method of signal is gaven.The detail signals on each scale are further more decomposed with wavelet transform.The subdetail signals and subsmoothing signals are processed with different threshold respectively. The smoothing signals on the coarsest scale are processed with Kalman fitering and reconstructed with the detail signal on each scale.At last the signal estimate value on the original scale is obtained.展开更多
For an arbitrary class of rings M, we have studied, in this paper, some necessary and sufficient conditions for ψM to be closed under homomorphic images or essential extensions, or to be a semisimple class or heredit...For an arbitrary class of rings M, we have studied, in this paper, some necessary and sufficient conditions for ψM to be closed under homomorphic images or essential extensions, or to be a semisimple class or hereditary class. The main results are: Theorem 4.1 For an arbitrary class of rings M, the following are equivalent: (1) M is a semisimple class; (2) ψM = ψuψM; (3) M~*=(uψM)~*; (4) M^(**)■M~*■(uψM)~*. Theorem 4.3 For an arbitray class of rings M, the follawing are equivalent: (1) ψM is the semisimple class of a hereditary radical; (2) ψM is an essentially closed semisimple class; (3) M~*=(uψM)~* and M~* is essentially hereditary; (4) M~*=(uψM)~* and uψM is essentially hereditary; (5)M~*=(uψM)~* and ψM is essentially closed.展开更多
In this paper,the I-ring which satisfies almost descending chain conditions (shorten writting A. D. C. C) on principal left ideals is studied. Two main results are gaven: (1) I-ring which satisfies A. D.C. C on princi...In this paper,the I-ring which satisfies almost descending chain conditions (shorten writting A. D. C. C) on principal left ideals is studied. Two main results are gaven: (1) I-ring which satisfies A. D.C. C on principal left ideals is Boolen. (2) Ring with identity whose principal left ideals satisfy A. D. C. C and of which each element except identity is a left zero-divisor, is Boolean.These results generalize the results of [1],[2] and [3].展开更多
文摘A Class of rings is said to be weakly hereditary if 0≠I△R∈ implies 0≠I^n∈ for some positive integer n, which generalizes the concept of heredity but other than that of regularity. In §2 the properties of such class and its essential cover are studied. In §3 the upper radicals determined by them are investigated. At the same time the 'Problem 42, 44 and 55' of Szasz [7] are discussed. In §4 two examples are given, which show that the concept of weak heredity is independent of that of regularity.
文摘In this paper an improved multi_scale estimation method of signal is gaven.The detail signals on each scale are further more decomposed with wavelet transform.The subdetail signals and subsmoothing signals are processed with different threshold respectively. The smoothing signals on the coarsest scale are processed with Kalman fitering and reconstructed with the detail signal on each scale.At last the signal estimate value on the original scale is obtained.
文摘For an arbitrary class of rings M, we have studied, in this paper, some necessary and sufficient conditions for ψM to be closed under homomorphic images or essential extensions, or to be a semisimple class or hereditary class. The main results are: Theorem 4.1 For an arbitrary class of rings M, the following are equivalent: (1) M is a semisimple class; (2) ψM = ψuψM; (3) M~*=(uψM)~*; (4) M^(**)■M~*■(uψM)~*. Theorem 4.3 For an arbitray class of rings M, the follawing are equivalent: (1) ψM is the semisimple class of a hereditary radical; (2) ψM is an essentially closed semisimple class; (3) M~*=(uψM)~* and M~* is essentially hereditary; (4) M~*=(uψM)~* and uψM is essentially hereditary; (5)M~*=(uψM)~* and ψM is essentially closed.
文摘In this paper,the I-ring which satisfies almost descending chain conditions (shorten writting A. D. C. C) on principal left ideals is studied. Two main results are gaven: (1) I-ring which satisfies A. D.C. C on principal left ideals is Boolen. (2) Ring with identity whose principal left ideals satisfy A. D. C. C and of which each element except identity is a left zero-divisor, is Boolean.These results generalize the results of [1],[2] and [3].
