THE OSOFSKY-SMITH THEOREM FOR MODULAR LATTICES, AND APPLICATIONS (II)

Toma Albu

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THE OSOFSKY-SMITH THEOREM FOR MODULAR LATTICES, AND APPLICATIONS (II)

机译：模格的OSOFSKY-SMITH定理及应用（二）

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This is the second part of the paper with the same title published in Communications in Algebra in 2011. It contains applications of the Latticial Osofsky-Smith Theorem to Grothendieck categories and module categories equipped with a torsion theory. Various many different meanings spread in the literature of the relative concepts with respect to a hereditary torsion theory τ on Mod-R like τ-essential submodule, τ-complement submodule, τ-CS module, etc. are also discussed.

机译：这是该论文的第二部分，标题相同，该论文于2011年在《代数通讯》中发表。该论文包含莱索托夫·奥索夫斯基-史密斯定理在格洛腾迪克类别和配有扭转理论的模块类别中的应用。还讨论了有关相对于Mod-R的遗传扭转理论τ的各种概念，其中包括τ基本子模块，τ互补子模块，τ-CS模块等。

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《Communications in algebra》 |2014年第6期|共21页
作者
Toma Albu;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Finitely generated object; Grothendieck category; Locally finitely generated category; The Categorical Osofsky-Smith Theorem; The Latticial Osofsky-Smith Theorem; The Relative Osofsky-Smith Theorem; Torsion theory; τ-CS module; τ-Compact module; τ-Compactly generated module; τ-Finitely generated module;

机译：有限生成的对象;Grothendieck类;局部有限生成的类;分类Osofsky-Smith定理;格Osofsky-Smith定理;相对Osofsky-Smith定理;扭转理论;τ-CS模块;τ-紧凑模块;τ-紧凑生成模块;τ有限生成的模块;

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1. 关于半模格的一个特征定理 [J] . 马占新东北数学：英文版 . 1999,第004期
2. THE OSOFSKY-SMITH THEOREM FOR MODULAR LATTICES, AND APPLICATIONS (II) [J] . Toma Albu Communications in algebra . 2014,第5a6期

机译：模格的OSOFSKY-SMITH定理及应用（二）
3. Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes [J] . Antonio Boccuto, Domenico Candeloro, Anna Rita Sambucini Journal of Mathematical Analysis and Applications . 2014,第2期

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5. Decomposition theorems and representation theorems of lattice interval value Fuzzy sets (VII) [C] . Zhan Xueqiu Fuzzy Systems and Knowledge Discovery (FSKD), 2012 9th International Conference on . 2012

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6. Residue number system's (RNS) non-modular operations efficient implementation based on Chinese remainder theorem II (CRT II). [D] . Al-Radadi, Eid Ayad. 2002

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7. Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications [O] . Godwin Amechi Okeke, Daniel Francis, Manuel de la Sen 2020

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8. Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes [O] . Boccuto, Antonio, Candeloro, Domenico, Sambucini, Anna Rita 2014

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9. Cardinal Interpolation and Spline Functions VIII. The Budan-Fourier Theorem for Splines and Applications. [R] . de Boor, C., Schoenberg, I. J. 1975

机译：基数插值和样条函数VIII。样条和应用的Budan-Fourier定理。

THE OSOFSKY-SMITH THEOREM FOR MODULAR LATTICES, AND APPLICATIONS (II)

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