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National Repository of Grey Literature 2 records found  Search took 0.02 seconds. 
Tall rings
 Penk, Tomáš ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
Perfect and max rings are known for over fifty years. Their theory is being steadily and intensively studied. The conditions defining them are mainly interesting while studying non-noetherian modules. In this work we summarize at first basic information about rings and modules with previous knowledge requiring just in elementary level. After summing up basic results in the theory of noetherian modules we will be prepaired for the definition of tall modules and tall rings. We show then that they are a generalization of prefect and max rings in a specific way. We bring out some examples of tall and non-tall rings with accenting commutative rings. Information which we obtain we try to generalize and use for searching some necessary and some sufficient conditions with the goal to be able to say about a commutative ring if it is tall or not. At the end we point out that in case of a commutative noetherian ring they are equivalent to each other and they give together to the concept tall ring an equivalent characterization.
Detailed record
Tall rings
 Penk, Tomáš ; Žemlička, Jan (advisor) ; Šťovíček, Jan (referee)
Perfect and max rings are known for over fifty years. Their theory is being steadily and intensively studied. The conditions defining them are mainly interesting while studying non-noetherian modules. In this work we summarize at first basic information about rings and modules with previous knowledge requiring just in elementary level. After summing up basic results in the theory of noetherian modules we will be prepaired for the definition of tall modules and tall rings. We show then that they are a generalization of prefect and max rings in a specific way. We bring out some examples of tall and non-tall rings with accenting commutative rings. Information which we obtain we try to generalize and use for searching some necessary and some sufficient conditions with the goal to be able to say about a commutative ring if it is tall or not. At the end we point out that in case of a commutative noetherian ring they are equivalent to each other and they give together to the concept tall ring an equivalent characterization.
Detailed record

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