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a note on g-type rings
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نویسنده
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moslemi bahman ,soltanpour somayeh
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منبع
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مدل سازي پيشرفته رياضي - 2024 - دوره : 14 - شماره : 3 - صفحه:71 -78
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چکیده
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In this article, we introduce and examine the concept of g-type rings. a ring r is classied as a g-type ring if its total quotient ring, denoted by q, is generated by a countable number of elements over r as an r-algebra. formally, q = r[s1], wheres is a countable set of regular elements in r. we establish that r is g-type if and onlyif there exists a countable set of regular elements, denoted as s, such that every primeideal disjoint from s consists solely of zero-divisors. it is shown that whenever a ring tis countably generated over a subring r, as an r-algebra, and t is strongly algebraic over r, then r is g-type if and only if t is g-type.
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کلیدواژه
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total quotient ring ,g-type ring ,g-type ideal ,caliber ,strongly algebraic.
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آدرس
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petroleum university of technology, ahvaz faculty of petroleum, department of basic science, iran, petroleum university of technology, ahvaz faculty of petroleum, department of basic science, iran
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پست الکترونیکی
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s.soltanpour@put.ac.ir
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a note on g-type rings
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Authors
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Abstract
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in this article, we introduce and examine the concept of g-type rings. a ring r is classied as a g-type ring if its total quotient ring, denoted by q, is generated by a countable number of elements over r as an r-algebra. formally, q = r[s1], wheres is a countable set of regular elements in r. we establish that r is g-type if and onlyif there exists a countable set of regular elements, denoted as s, such that every primeideal disjoint from s consists solely of zero-divisors. it is shown that whenever a ring tis countably generated over a subring r, as an r-algebra, and t is strongly algebraic over r, then r is g-type if and only if t is g-type.
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Keywords
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total quotient ring ,g-type ring ,g-type ideal ,caliber ,strongly algebraic.
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