On inverse operations in the lattices of submodules
In the lattice L(RM) of submodules of an arbitrary left R-module RM four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for α-product and ω-coproduct) are defined and studied. Some properties of l...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152210 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On inverse operations in the lattices of submodules / A.I. Kashu // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 2. — С. 273–288. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In the lattice L(RM) of submodules of an arbitrary left R-module RM four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for α-product and ω-coproduct) are defined and studied. Some properties of left quotient with respect to α-product and right quotient with respect to ω-coproduct are shown, as well as their relations with the lattice operations in L(RM) (sum and intersection of submodules). The particular case RM = RR of the lattice L(RR) of left ideals of the ring R is specified.
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| ISSN: | 1726-3255 |