Flat modules over formal matrix rings
WebMar 31, 2024 · We set out the basic theory of modules over formal matrix rings and consider the structure of some submodules (small and essential submodules, the socle and the radical). We pay much attention to injective, flat and projective modules over formal matrix rings of order 2. WebOct 22, 2010 · Modules over formal matrix rings P. A. Krylov & A. A. Tuganbaev Journal of Mathematical Sciences 171 , 248–295 ( 2010) Cite this article 272 Accesses 27 Citations Metrics Abstract This work contains some new and known results on modules over formal matrix rings. The main results are presented with proofs. Download to read the full …
Flat modules over formal matrix rings
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WebApr 1, 2024 · Gorenstein flat modules and dimensions over formal triangular matrix rings Recall that a left R -module M is Gorenstein flat [4], [5] if there is an exact sequence ⋯ … WebDec 15, 2024 · Let be a formal triangular matrix ring, where and are rings and is a -bimodule. We prove that: (1) If and have finite flat dimensions, then a left -module is …
WebAbstract. Let T=\bigl (\begin {smallmatrix}A&0\\U&B\end {smallmatrix}\bigr) T = (A U 0 B) be a formal triangular matrix ring, where A A and B B are rings and U U is a (B, A) (B,A) -bimodule. We prove: (1) If U_ {A} U A and _ {B}U BU have finite flat dimensions, then a left T T -module \bigl (\begin {smallmatrix}M_1\\ M_2\end {smallmatrix}\bigr ... WebMar 3, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
WebKey Words: Formal triangular matrix ring, strongly Gorenstein projective module, strongly Gorenstein injective module, strongly Gorenstein flat module. 2010 Mathematics Subject Classification: Primary 16D40, 16D90, 16E05. Download the paper in pdf format
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WebNov 20, 2006 · Let A and B be two rings, M be a left B , right A bimodule and be the formal triangular matrix ring. It is known that the category of right T -modules is equivalent to the category Ω of triples ( X , Y ) f , where X is a right A -module, Y is a right B -module and is a right A -homomorphism. Using this alternative description of right T -modules, in the first … olympus cndWebLet T=\bigl (\begin {smallmatrix}A&0\\U&B\end {smallmatrix}\bigr) T = (A U 0 B) be a formal triangular matrix ring, where A A and B B are rings and U U is a (B, A) (B,A) -bimodule. … is anthem avm 70 roon readyWebJan 1, 2024 · PDF On Jan 1, 2024, 淑娴 薛 published PGF Modules over Formal Triangular Matrix Rings Find, read and cite all the research you need on ResearchGate is anthem and cigna the sameWebPURE PROJECTIVITY AND PURE INJECTIVITY OVER FORMAL TRIANGULAR MATRIX RINGS. Journal of Algebra and Its Applications, Vol. 11, Issue. 06, p. 1250107. ... more advanced topics, such as hereditary rings, categories and functors, flat modules and purity are introduced. These later chapters will also prove a useful reference for researchers in … olympus cm10 cameraWebJun 1, 2024 · Formal triangular matrix rings play an important role in ring theory and the representation theory of algebra. This kind of rings are often used to construct important examples and counterexamples, which make the theory of rings and modules more abundant and concrete. is anthem and bcbs the sameWebProvides the first systematic treatment of formal matrices in a single volume Examines injective, flat, projective and hereditary modules over formal matrix rings of order 2 in … olympus cnc machineWebMar 24, 2024 · A module M over a unit ring R is called flat iff the tensor product functor - tensor _RM (or, equivalently, the tensor product functor M tensor _R-) is an exact … olympus clv 160 service manual