《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (4): 67-73.doi: 10.6040/j.issn.1671-9352.0.2019.007
• • 上一篇
尹娇娇,邵勇*,韩金
YIN Jiao-jiao, SHAO Yong*, HAN Jin
摘要： 探究了交换反环上的e-可逆矩阵,给出了交换反环上e-可逆矩阵的等价刻画,揭示了交换反环上的某个半线性空间上的半线性变换与e-可逆矩阵之间的关系。
中图分类号:
| [1] 张后俊, 储茂权. 交换半环上半线性空间的维数[J].山东大学学报(理学版),2015,50(6):45-52. ZHANG Houjun, CHU Maoquan. Dimensions of semilinear spaces over commutative semirings[J]. Journal of Shandong University(Natural Science), 2015, 50(6):45-52. [2] 许格妮, 李永明. 转移函数保半环赋值代数轮廓解的条件[J]. 山东大学学报(理学版), 2015, 50(8):51-56. XU Geni, LI Yongming. On conditions for transfer function to preserve solution configuration of semiring-induced valuation algebras[J]. Journal of Shandong University(Natural Science), 2015, 50(8):51-56. [3] 王凌云. 半环上的分配格同余[J]. 山东大学学报(理学版), 2009, 44(9):63-65. WANG Lingyun. Distributive congruences on semirings[J]. Journal of Shandong University(Natural Science), 2009, 44(9):63-65. [4] GOLAN J S. Semirings and their applications[M]. London: Kluwer Academic Publishers, 1999. [5] REUTENAUER C, STRAUBING H. Inversion of matrices over a commutative semiring[J]. Journal of Algebra, 1984, 88(2):350-360. [6] 朱丽, 赵建东. 利用可逆矩阵进行加密算法初探[J]. 中国电子商务, 2014(12):90-90. ZHU Li, ZHAO Jiandong. A preliminary study on encryption algorithms using invertible matrix[J]. Discovering Value, 2014, 12:90-90. [7] TAN Yijia. On invertible matrices over commutative semirings[J]. Linear and Multilinear Algrbra, 2013, 61(6):710-724. [8] SIRASUNTORN N, UDOMSUB N. Inversion of matrices over Boolean semirings[J]. Thai Journal of Mathematices, 2009, 7(1):105-113. [9] GAUJAL B, JEAN-MARIE A. Computational issues in recursive stochastic systems[J]. Idempotency, 1998: 209-230. [10] PSHENITSYNA O A. Mappings that preserve the invertibility of matrices over semirings[M]. [S.l.] : Translation in Russian Math Surveys, 2009, 64:162-164. [11] BACCELLI F L, MAIRESSE I. Ergodic theorems for stochastic operators and discrete event networks[J]. Idempotency, 1998, 11:171-208. [12] MORA W, WASANAWICHIT A, KEMPRASIT Y. Invertible matrices over idempotent semirings[J]. Chamchuri Journal of Mathematices, 2009, 1(2):55-61. [13] 张丽梅, 乔立山, 李莹. 可逆坡矩阵与坡矩阵的秩[J]. 山东大学学报(理学版), 2007, 42(9):122-126. ZHANG Limei, QIAO Lishan, LI Ying. Invertible incline matrices and ranks of incline matrices[J]. Journal of Shandong University(Natural Science), 2007, 42(9):122-126. [14] ZHANG Lixia, SHAO Yong. e-Invertible matrices over commutative semirings[J]. Indian Journal of Pure and Applied Mathematics, 2018, 49(2):227-238. [15] VECHTOMOV E M. Two general structure theorems on submodules, Abelian group and modules[J]. Tomsk State University, 2000, 15:17-23. [16] LUCE R D. A note on Boolean matrix theory[J]. Proceedings of the American Mathematical Society, 1952, 3(3):382-388. [17] GIVEON Y. Lattice matrices[J]. Information and Control, 1964, 7:477-484. [18] ZHAO Cuikui. Invertible conditions for a matrix over distributive lattice[J]. Acta Scientiarum Naturalium Universitatis Neimongol, 1991, 22(4):477-480. [19] 赵飏. 模糊矩阵的逆[J]. 辽宁教育学院学报, 1998, 15(5):37-37. ZHAO Yang. Inverse of fuzzy matrix[J]. Journal of Liaoning Educational Institute, 1998, 15(5):37-37. [20] TAN Yijia. On invertible matrices over antirings[J]. Linear Algrbra and Its Applications, 2007, 423(2):428-444. [21] 张丽霞, 邵勇. 关于交换半环上一类矩阵的研究[J]. 计算机工程与应用, 2017, 53(20):56-60. ZHANG Lixia, SHAO Yong. Study on a class of matrices over commutative semirings[J]. Computer Engineering and Applications, 2017, 53(20):56-60. |
|
||
