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
Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on...Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on atoms, pseudo O-linear and O-linear strategies are presented. The former is complete, the latter,however, is complete for clausal theorem proving.展开更多
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].
文摘Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on atoms, pseudo O-linear and O-linear strategies are presented. The former is complete, the latter,however, is complete for clausal theorem proving.
