Commutative feebly invo-clean group rings P. V. Danchev
Material type:
ArticleOther title: Коммутативные мало инво-чистые групповые кольца [Parallel title]Subject(s): инво-чистые кольца | слабо инво-чистые кольца | мало инво-чистые кольца | групповые кольцаGenre/Form: статьи в журналах Online resources: Click here to access online
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Вестник Томского государственного университета. Математика и механика № 61. С. 5-10Abstract: A commutative ring R is called feebly invo-clean if any its element is of the form v+e− f , where v is an involution and e, f are idempotents. For every commutative unital ring R and every abelian group G we find a necessary and sufficient condition only in terms of R , G and their sections when the group ring R[G] is feebly invo-clean. Our result improves two recent own achievements about commutative invo-clean and weakly invo-clean group rings, published in Univ. J. Math. & Math. Sci. (2018) and Ural Math. J. (2019), respectively.
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A commutative ring R is called feebly invo-clean if any its element is of the form v+e− f , where v is an involution and e, f are idempotents. For every commutative unital ring R and every abelian group G we find a necessary and sufficient condition only in terms of R , G and their sections when the group ring R[G] is feebly invo-clean. Our result improves two recent own achievements about commutative invo-clean and weakly invo-clean group rings, published in Univ. J. Math. & Math. Sci. (2018) and Ural Math. J. (2019), respectively.
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