Subring of a Ring - Definition & Example - Ring Theory - Algebra

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What is a Subring ?
, i will explain this definition in today's video with some examples.
which is a very important topic of Ring Theory
everything is explained in Hindi
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This video will be very useful if you are student of Higher Classes in mathematics like B.Sc, M.Sc , Engineering and if you are preparing for UGC Net and iit Jam etc.
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Before this topic i did various other topics of Real Analysis:
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• Lower Bound, GLB and I... cyclic vbv

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[@mohdtalhakhan7859]

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[@user-jo2xj9dt1v]

I work in Algebraic geometry, with theoretical examples of a Noeterian ring. For example, consider every closed-map of $R^{n}\to{} R^{n+1}$, in general $R^{n}$ has a closed ring since any point $p$ is a limit on spaces of $R^{n}$ .
But if it is Noeterian, can every point $p$ of a Lie-maximal Group "be simple and compact in $R^{n}$ ? , or can the morphism of a closed-map be fulfilled in $R^{ n}\to{} G(R^{n+1}) ? .
In general, if the ring of $R^{n}$ is Noeterian, it is true that $R^{n}\to{} R^{m}$ or a subspace of $R^{n}$ Which also writes the Noeterian ring as the subring of $R^{n}$ (In general for a Noeterian ring, not every point $p$ is a limit of $R^{n}$ If not for limits that correspond to a subspace "or subring" in $R^{m}$

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For this reason, the Noetherian ring "discriminant of $R^{n}$ is local with a Riemannian metric in each given Tangent-space $T(M)\otimes{} T^{*}$

[@preetikumari6611]

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[@Ssc2969]

Mam thanks for your videos. Just a question - Shouldn't subring contain UNITY elements too ?

[@learnmatheasily]

Not necessary

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Thank you so much mam